Carlos Egues

Magneto-oscillations in two-dimensional systems with spin-orbit interaction are typically characterized by fast Shubnikov-de~Haas (SdH) oscillations and slower spin-orbit-related beatings. The characterization of the full SdH oscillatory behavior in systems with both spin-orbit interaction and Zeeman coupling requires a time consuming diagonalization of large matrices for many magnetic field values. By using the Poisson summation formula we can explicitly separate the density of states into, fast and slow oscillations, which determine the corresponding fast and slow parts of the magneto-oscillations. We introduce an efficient scheme of partial diagonalization of our Hamiltonian, where only states close to the Fermi energy are needed to obtain the SdH oscillations, thus reducing the required computational time. This allows an efficient method for fitting numerically the SdH data, using the inherent separation of the fast and slow oscillations. We compare systems with only Rashba spin-orbit interaction (SOI) and both Rashba and Dresselhaus SOI with, and without, an in-plane magnetic field. The energy spectra are characterized in terms of symmetries, which have direct and visible consequences in the magneto-oscillations. To highlight the benefits of our methodology, we use it to extract the spin-orbit parameters by fitting realistic transport data.

Shubnikov-de Haas (SdH) oscillations are the fingerprint of the Landau and Zeeman splitting level structure on the resistivity in presence of a moderate magnetic field before full quantization is manifest in the integer quantum Hall effect. These oscillations have served as a paradigmatic experimental probe and tool for extracting key semiconductor parameters such as carrier density, effective mass $m^*$, Zeeman splitting with g-factor $g^*$, quantum scattering time and Rashba $\alpha$ and Dresselhaus $\beta$ spin-orbit (SO) coupling parameters. Analytical descriptions of the SdH oscillations are available for some special cases, but the generic case with all three terms simultaneously present has not been solved analytically so far, seriously hampering the analysis and interpretation of experimental data. Here, we bridge this gap by providing an analytical formulation for the SdH oscillations of 2D electron gases (2DEGs) with simultaneous and arbitrary Rashba, Dresselhaus, and Zeeman interactions. We use a Poisson summation formula for the density of states of the 2DEG, which affords a complete yet simple description of the oscillatory behavior of its magnetoresistivity. Our analytical and numerical calculations allow us to extract the beating frequencies, quantum lifetimes, and also to understand the role of higher harmonics in the SdH oscillations. More importantly, we derive a simple condition for the vanishing of SO induced SdH beatings for all harmonics in 2DEGs: $\alpha/\beta= [(1-\tilde \Delta)/(1+\tilde \Delta)]^{1/2}$, where $\tilde \Delta\propto g^* m^*$ is a material parameter given by the ratio of the Zeeman and Landau level splitting. This condition is notably different from that of the persistent spin helix at $\alpha/\beta=1$ for materials with large $g^*$ such as InAs or InSb. We also predict beatings in the higher harmonics of the SdH oscillations and elucidate the inequivalence of the SdH response of Rashba-dominated ($\alpha>\beta$) vs Dresselhaus-dominated ($\alpha<\beta$) 2DEGs in semiconductors with substantial $g^*$. We find excellent agreement with recent available experimental data of Dettwiler {\it et al.} Phys. Rev. X \textbf{7}, 031010 (2017), and Beukman {\it et al.}, Phys. Rev. B \textbf{96}, 241401 (2017). The new formalism builds the foundation for a new generation of quantum transport experiments and spin-orbit materials with unprecedented physical insight and material parameter extraction.

Identifying topological phases via zero-bias conductance peaks in Majorana wires is not trivial. Here we address this issue in realistic three-terminal proximitized superconducting (disordered) nanowires coupled to normal leads, purportedly capable of hosting (quasi-) zero-energy Majorana modes. By using Green functions and the scattering matrix formalism, we calculate the conductance matrix and the local density of states (LDOS) for asymmetrically tunnel coupled left (ΓL, constant) and right (ΓR) leads. In the trivial phase, we find that the local conductances are distinctively affected by variations in ΓR: while GLL is essentially constant, GRR is exponentially suppressed as ΓR diminishes. In the topological phase (bulk criterion), surprisingly, GLL and GRR are suppressed in the exact same way, i.e., GLL=GRR. This nonlocal suppression of GLL scales with the hybridization between the Majorana zero modes (MZMs) and arises from the emergence of a dip in the LDOS around zero energy at the left end of the wire, which in turn affects the MZM-mediated local Andreev reflections. We also present a Majorana transistor exploiting the nonlocality of the local Andreev processes and the gate-controlled suppression of the LDOS. Finally, we propose a protocol for distinguishing trivial from topological zero-bias peaks that rely only on local conductance measurements.

The spin-orbit interaction in spin qubits enables spin-flip transitions, resulting in Rabi oscillations when an external microwave field is resonant with the qubit frequency. Here, we introduce an alternative driving mechanism of hole spin qubits, where a far-detuned oscillating field couples to the qubit phase. Phase driving at radio frequencies, orders of magnitude slower than the microwave qubit frequency, induces highly non-trivial spin dynamics, violating the Rabi resonance condition. By using a qubit integrated in a silicon fin field-effect transistor (Si FinFET), we demonstrate a controllable suppression of resonant Rabi oscillations, and their revivals at tunable sidebands. These sidebands enable alternative qubit control schemes using global fields and local far-detuned pulses, facilitating the design of dense large-scale qubit architectures with local qubit addressability. Phase driving also decouples Rabi oscillations from noise, an effect due to a gapped Floquet spectrum and can enable Floquet engineering high-fidelity gates in future quantum processors

When normal metals (NMs) are attached to topological insulators or topological superconductors, it is conceivable that the quantum states in these finite adjacent materials can intermix. In this case -- and because the NM usually does not possess the same symmetry as the topological material -- it is pertinent to ask whether zero-energy edge states in the topological layer are affected by the presence of the NM. To address this issue, we consider three prototype systems simulated by tight-binding models, namely a Su-Schrieffer-Heeger/NM, a Kitaev/NM, and a Chern insulator/NM. For all junctions investigated, we find that there exist trivial "fine-tuned" zero-energy states in the NM layer that can percolate into the topological region, thus mimicking a topological state. These zero-energy states are created by fine-tuning the NM chemical potential such that some of the NM states cross zero energy; they can occur even when the topological material is in the topologically trivial phase. Interestingly, the true Majorana end modes of the Kitaev/NM model cannot be crossed by any NM state, as the NM metal layer in this case does not break particle-hole symmetry. On the other hand, when the chiral symmetry of the Su-Schrieffer-Heeger chain is broken by the attached NM, crossings are allowed. In addition, even in Chern insulators that do not preserve non-spatial symmetries, but the topological edge state self-generates a symmetry eigenvalue, such a fine-tuned zero-energy state can still occur. Our results indicate that when a topological material is attached to a metallic layer, one has to be cautious as to identify true topological edge states merely from their energy spectra and wave function profiles near the interface.

We study the transitions between ergodic and many-body localized phases in spin systems, subject to quenched disorder, including the Heisenberg chain and the central spin model. In both cases systems with common spin lengths 1/2 and 1 are investigated via exact numerical diagonalization and random matrix techniques. Particular attention is paid to the sample-to-sample variance (Δsr)2 of the averaged consecutive-gap ratio ⟨r⟩ for different disorder realizations. For both types of systems and spin lengths we find a maximum in Δsr as a function of disorder strength, accompanied by an inflection point of ⟨r⟩, signaling the transition from ergodicity to many-body localization. The critical disorder strength is found to be somewhat smaller than the values reported in the recent literature. Further information about the transitions can be gained from the probability distribution of expectation values within a given disorder realization.

We perform momentum-conserving tunneling spectroscopy using a GaAs cleaved-edge overgrowth quantum wire to investigate adjacent quantum Hall edge states. We use the lowest five wire modes with their distinct wave functions to probe each edge state and apply magnetic fields to modify the wave functions and their overlap. This reveals an intricate and rich tunneling conductance fan structure which is succinctly different for each of the wire modes. We self-consistently solve the Poisson-Schrödinger equations to simulate the spectroscopy, reproducing the striking fans in great detail, thus confirming the calculations. Further, the model predicts hybridization between wire states and Landau levels, which is also confirmed experimentally. This establishes momentum-conserving tunneling spectroscopy as a powerful technique to probe edge state wave functions.

Motivated by recent experiments, we investigate the quantum spin Hall state in 2D topological insulator/ferromagnetic metal planar junctions by means of a tight-binding model and linear response theory. We demonstrate that whether the edge state Dirac cone is submerged into the ferromagnetic subbands and the direction of the magnetization dramatically affect how the edge state percolates into the ferromagnet. Despite the percolation, spin-momentum locking of the edge state remains robust in the topological insulator region. In addition, laminar flows of room temperature persistent charge and spin currents near the interface are uncovered, and the current-induced spin torque is found to be entirely field-like due to the real wave functions of the percolated edge state and the quantum well state of the ferromagnet.

Effective spin-orbit (SO) Hamiltonians for conduction electrons in wurtzite heterostructures are lacking in the literature, in contrast to zincblende structures. Here we address this issue by deriving such an effective Hamiltonian valid for quantum wells, wires, and dots with arbitrary confining potentials and external magnetic fields. We start from an 8×8 Kane model accounting for the s--pz orbital mixing important to wurtzite structures, but absent in zincblende, and apply both quasi-degenerate perturbation theory (Löwdin partitioning) and the folding down approach to derive an effective 2×2 electron Hamiltonian. We obtain the usual k-linear Rashba term arising from the structural inversion asymmetry of the wells and, differently from zincblende structures, a bulk Rashba-type term induced by the inversion asymmetry of the wurtzite lattice. We also find linear- and cubic-in-momentum Dresselhaus contributions. Both the bulk Rashba-type term and the Dresselhaus terms originate exclusively from the admixture of s- and pz-like states in wurtzites structures. Interestingly, in these systems the linear Rashba and the Dresselhaus terms have the same symmetry and can in principle cancel each other out completely, thus making the spin a conserved quantity. We determine the intrasubband (intersubband) Rashba αν (η) and linear Dresselhaus βν (Γ) SO strengths of GaN/AlGaN single and double wells with one and two occupied subbands (ν=1,2). We believe our general effective Hamiltonian for electrons in wurtzite heterostructures put forward here, should stimulate additional theoretical works on wurtzite quantum wells, wires, and dots with variously defined geometries and external magnetic fields.

We present a Green's function formalism to investigate the topological properties of weakly interacting one-dimensional topological insulators, including the bulk-edge correspondence and the quantum criticality near topological phase transitions, and using interacting Su-Schrieffer-Heeger model as an example. From the many-body spectral function, we find that closing of the bulk gap remains a defining feature even if the topological phase transition is driven by interactions. The existence of edge state in the presence of interactions can be captured by means of a T-matrix formalism combined with Dyson's equation, and the bulk-edge correspondence is shown to be satisfied even in the presence of interactions. The critical exponent of the edge state decay length is shown to be affiliated with the same universality class as the noninteracting limit.

We derive a closed-form expression for the weak localization (WL) corrections to the magnetoconductivity of a 2D electron system with arbitrary Rashba α and Dresselhaus β (linear) and β3 (cubic) spin-orbit interaction couplings, in a perpendicular magnetic field geometry. In a system of reference with an in-plane ẑ axis chosen as the high spin-symmetry direction at α=β, we formulate a new algorithm to calculate the three independent contributions that lead to WL. The antilocalization is counterbalanced by the term associated with the spin-relaxation along ẑ , dependent only on α−β. The other term is generated by two identical scattering modes characterized by spin-relaxation rates which are explicit functions of the orientation of the scattered momentum. Excellent agreement is found with data from GaAs quantum wells, where in particular our theory correctly captures the shift of the minima of the WL curves as a function of α/β. This suggests that the anisotropy of the effective spin relaxation rates is fundamental to understanding the effect of the SO coupling in transport.

We investigate the ballistic Zitterbewegung dynamics and the Landau-Zener tunneling between edge and bulk states of wave packets in two-dimensional topological insulators. In bulk, we use the Ehrenfest theorem to show that an external in-plane electric field not only drifts the packet longitudinally, but also induces a transverse finite side-jump for both trivial and topological regimes. For finite ribbons of width W, we show that the Landau-Zener tunneling between bulk and edge states vanishes for large W as their electric field-induced coupling decays with W−3/2. This is demonstrated by expanding the time-dependent Schr\"odinger equation in terms of Houston states. Hence we cannot picture the quantum spin Hall states as arising from the Zitterbewegung bulk trajectories `leaking' into the edge states as proposed in Phys. Rev. B 87, 161115 (2013).

We present a paradoxical finding that, in the vicinity of a topological phase transition in a quantum anomalous Hall system (Chern insulator), topology nearly always (except when the system obeys charge-conjugation symmetry) results in a significant extension of the edge-state structure beyond the minimal one required to satisfy the Chern numbers. The effect arises from the universal gapless linear-in-momentum Hamiltonian of the nodal semimetal describing the system right at the phase transition, whose form is enforced by the change of the Chern number. Its emergent approximate chiral symmetry results in an edge-state band in the vicinity of the node, in the region of momenta where such form is dominant. Upon opening the gap, this edge-state band is modified in the gap region, becoming "protected" (connected to the valence bulk band with one end and conduction band with the other) in the topologically nontrivial phase and "nonprotected" (connected to either the valence or conduction band with both ends) in the trivial phase. The edge-state band persists in the latter as long as the gap is small enough.

We investigate the electronic and transport properties of topological and trivial InAs1−xBix quantum dots (QDs). By considering the rapid band gap change within valence band anticrossing theory for InAs1−xBix, we predicted that Bi-alloyed quantum wells become ∼30meV gapped 2D topological insulators for well widths d>6.9nm (x=0.15) and obtain the k.p parameters of the corresponding Bernevig-Hughes-Zhang (BHZ) model. We analytically solve this model for cylindrical confinement via modified Bessel functions. For non-topological dots we find "geometrically protected" discrete helical edge-like states, i.e., Kramers pairs with spin-angular-momentum locking, in stark contrast with ordinary InAs QDs. For a conduction window with four edge states, we find that the two-terminal conductance G vs. the QD radius R and the gate Vg controlling its levels shows a double peak at 2e^2/h for both topological and trivial QDs. In contrast, when bulk and edge-state Kramers pairs coexist and are degenerate, a single-peak resonance emerges. Our results blur the boundaries between topological and non-topological phenomena for conductance measurements in small systems such as QDs. Bi-based BHZ QDs should also prove important as hosts to edge spin qubits.

We exploit the high-symmetry spin state obtained for equal Rashba and linear Dresselhaus interactions to derive a closed-form expression for the weak localization magnetoconductivity -- the paradigmatic signature of spin-orbit coupling in quantum transport. The small parameter of the theory is the deviation from the symmetry state introduced by the mismatch of the linear terms and by the cubic Dresselhaus term. In this regime, we perform quantum transport experiments in GaAs quantum wells. Top and back gates allow independent tuning of the Rashba and Dresselhaus terms in order to explore the broken-symmetry regime where the formula applies. We present a reliable two-step method to extract all parameters from fits to the new expression, obtaining excellent agreement with recent experiments. This provides experimental confirmation of the new theory, and advances spin-orbit coupling towards a powerful resource in emerging quantum technologies.

The Rashba and Dresselhaus spin-orbit (SO) interactions in 2D electron gases act as effective magnetic fields with momentum-dependent directions, which cause spin decay as the spins undergo arbitrary precessions about these randomly-oriented SO fields due to momentum scattering. Theoretically and experimentally, it has been established that by fine-tuning the Rashba α and Dresselhaus β couplings to equal {\it fixed} strengths α=β, the total SO field becomes unidirectional thus rendering the electron spins immune to dephasing due to momentum scattering. A robust persistent spin helix (PSH) has already been experimentally realized at this singular point α=β. Here we employ the suppression of weak antilocalization as a sensitive detector for matched SO fields together with a technique that allows for independent electrical control over the SO couplings via top gate voltage VT and back gate voltage VB. We demonstrate for the first time the gate control of β and the {\it continuous locking} of the SO fields at α=β, i.e., we are able to vary both α and β controllably and continuously with VT and VB, while keeping them locked at equal strengths. This makes possible a new concept: "stretchable PSHs", i.e., helical spin patterns with continuously variable pitches P over a wide parameter range. The extracted spin-diffusion lengths and decay times as a function of α/β show a significant enhancement near α/β=1. Since within the continuous-locking regime quantum transport is diffusive (2D) for charge while ballistic (1D) for spin and thus amenable to coherent spin control, stretchable PSHs could provide the platform for the much heralded long-distance communication ∼8−25 μm between solid-state spin qubits. )

We have studied the edge spin accumulation in a high mobility two-dimensional electron gas formed in a symmetric well with two subbands. This study is strongly motivated by the recent experiment of Hernandez et al. [Phys. Rev. B {\bf 88}, 161305(R) (2013)] who demonstrated the spin accumulation near the edges of a bilayer symmetric GaAs structure in contrast to no effect in a single-layer configuration. The intrinsic mechanism of the spin-orbit interaction we consider arises from the coupling between two subband states of opposite parities. We obtain a parametrically large magnitude of the edge spin density for the two-subband sample as compared to the usual single-subband structure. We show that the presence of a gap in the system, i.e., the energy separation Δ between the two subband bottoms, changes drastically the picture of the edge spin accumulation. Thus one can easily proceed from the regime of weak spin accumulation to the regime of strong one by varying the Fermi energy (electron density) and/or Δ. We estimate that by changing the gap Δ from zero up to 1÷2 K, the magnitude of the effect changes by three orders of magnitude. This opens up the possibility for the design of new spintronic devices.

A persistent spin helix (PSH) is a robust helical spin-density pattern arising in disordered 2D electron gases with Rashba α and Dresselhaus β spin-orbit (SO) tuned couplings, i.e., α=±β. Here we investigate the emergence of a Persistent Skyrmion Lattice (PSL) resulting from the coherent superposition of PSHs along orthogonal directions -- crossed PSHs -- in wells with two occupied subbands ν=1,2. Our calculation shows that the Rashba αν and Dresselhaus βν couplings can be simultaneously tuned to equal strengths but opposite signs, e.g., α1=β1 and α2=−β2. In this regime and away from band anticrossings, our non-interacting electron gas sustains a topologically non-trivial skyrmion-lattice spin-density excitation, which inherits the robustness against time-reversal conserving perturbations from its underlying crossed PSHs. We find that the spin relaxation rate due to the interband SO coupling is comparable to that of the cubic Dresselhaus term as a mechanism for the PSL decay. Near the anticrossing, the strong interband-induced spin mixing leads to unusual spin textures along the energy contours beyond those of the Rahsba-Dresselhaus bands. We consider realistic GaAs and InSb wells for possible experiments.

Here we present a protocol for generating Lissajous curves with a trapped ion by engineering Rashba- and the Dresselhaus-type spin-orbit interactions in a Paul trap. The unique anisotropic Rashba αx, αy and Dresselhaus βx, βy couplings afforded by our setup also enables us to obtain an "unusual" Zitterbewegung, i.e., the semiconductor analog of the relativistic trembling motion of electrons, with cycloidal trajectories in the absence of magnetic fields. We have also introduced bounded SO interactions, confined to an upper-bound vibrational subspace of the Fock states, as an additional mechanism to manipulate the Lissajous motion of the trapped ion. Finally, we accounted for dissipative effects on the vibrational degrees of freedom of the ion and find that the Lissajous trajectories are still robust and well defined for realistic parameters.

We have recently shown [Phys. Rev. B {\bf 89}, 165314 (2013)] that a non--interacting quantum dot coupled to a 1D topological superconductor can sustain a Majorana mode even when the dot charge is removed by a gate voltage. This is due to the Majorana bound state of the wire leaking into the quantum dot. Here we extend this previous work by investigating the low--temperature quantum transport through an {\it interacting} quantum dot connected to source and drain leads and side--coupled to a topological wire. We explore the signatures of a Majorana zero--mode leaking into the quantum dot for a wide range of dot parameters, using a recursive Green's function approach. We then study the Kondo regime using numerical renormalization group calculations. We observe the interplay between the Majorana mode and the Kondo effect for different dot--wire coupling strengths, gate voltages and Zeeman fields. Our results show that a "0.5" conductance signature appears in the dot due to the presence of the Majorana mode, and that it persists for a wide range of dot parameters. The Kondo effect, on the other hand, is suppressed by both Zeeman fields and gate voltages. We show that the zero--bias conductance as a function of the magnetic field follows a well--known universality curve. This can be measured experimentally, and we propose that the universal conductance drop followed by a persistent conductance of 0.5e2/h are evidence for the presence of Majorana--Kondo physics. These results confirm that the Majorana signature in the dot remains even in the presence of the Kondo effect.

We investigate the Rashba and Dresselhaus spin-orbit (SO) couplings in GaAs quantum wells in the range of well widths w allowing for a transition of the electron occupancy from one to two subbands. By performing a detailed Poisson-Schr\"odinger self-consistent calculation, we determine all the intra- and inter-subband Rashba (α1, α2, η) and Dresselhaus (β1, β2, Γ) coupling strengths. For relatively narrow wells with only one subband occupied, our results are consistent with the data of Koralek \emph{et al.} [Nature \bfs{48}, 610 (2009)], i.e., the Rashba coupling α1 is essentially independent of w in contrast to the decreasing linear Dresselhaus coefficient β1. When we widen the well so that the second subband can also be populated, we observe that α2 decreases and α1 increases, both almost linearly with w. Interestingly, we find that in the parameter range studied (i.e., very asymmetric wells) α2 can attain zero and change its sign, while α1 is always positive. In this double-occupancy regime of w's, β1 is mostly constant and β2 decreases with w (similarly to β1 for the single-occupancy regime). On the other hand, the intersubband Rashba coupling strength η decreases with w while the intersubband Dresselhaus Γ remains almost constant. We also determine the persistent-spin-helix symmetry points, at which the Rashba and the renormalized (due to cubic corrections) linear Dresselhaus couplings in each subband are equal, as a function of the well width and doping asymmetry. Our results should stimulate experiments probing SO couplings in multi-subband wells.

The spin-orbit (SO) interaction couples electron spin and momentum via a relativistic, effective magnetic field. While conveniently facilitating coherent spin manipulation in semiconductors, the SO interaction also inherently causes spin relaxation. A unique situation arises when the Rashba and Dresselhaus SO fields are matched, strongly protecting spins from relaxation, as recently demonstrated. Quantum computation and spintronics devices such as the paradigmatic spin transistor could vastly benefit if such spin protection could be expanded from a single point into a broad range accessible with in-situ gate-control, making possible tunable SO rotations under protection from relaxation. Here, we demonstrate broad, independent control of all relevant SO fields in GaAs quantum wells, allowing us to tune the Rashba and Dresselhaus SO fields while keeping both locked to each other using gate voltages. Thus, we can electrically control and simultaneously protect the spin. Our experiments employ quantum interference corrections to electrical conductivity as a sensitive probe of SO coupling. Finally, we combine transport data with numerical SO simulations to precisely quantify all SO terms.

We show that electrons in ordinary III-V semiconductor double wells with an in-plane modulating periodic potential and inter well spin-orbit interaction are tunable Topological Insulators (TIs). Here the essential TI ingredients, namely, band inversion and the opening of an overall bulk gap in the spectrum arise, respectively, from (i) the combined effect of the double well even-odd state splitting $\Delta_{SAS}$ together with the superlattice potential and (ii) the interband Rashba spin-orbit coupling $\eta$. We corroborate our exact diagonalization results by an analytical nearly-free electron description that allows us to derive an effective Bernevig-Hughes-Zhang (BHZ) model. Interestingly, the gate-tunable $\Delta_{SAS}$ drives a topological phase transition featuring a discontinuous Chern number at $\Delta_{SAS}\sim 5.4$\, meV. Finally, we explicitly verify the bulk-edge correspondence by considering a strip configuration and determining not only the bulk bands in the non-topological and topological phases but also the edge states and their Dirac-like spectrum in the topological phase. The edge electronic densities exhibit peculiar spatial oscillations as they decay away into the bulk. For concreteness, we present our results for InAs-based wells with realistic parameters.

We investigate quantum transport through a quantum dot connected to source and drain leads and side coupled to a topological superconducting nanowire (Kitaev chain) sustaining Majorana end modes. Using a recursive Green's function approach, we determine the local density of states of the system and find that the end Majorana mode of the wire leaks into the dot thus emerging as a unique dot level pinned to the Fermi energy $\e_F$ of the leads. Quite surprisingly, this resonance pinning, resembling in this sense a "Kondo resonance", occurs even when the gate-controlled dot level $\e_\text{dot}(V_g)$ is far above or far below $\e_F$. The calculated conductance $G$ of the dot exhibits an unambiguous signature for the Majorana end mode of the wire: in essence, an off-resonance dot [$\e_\text{dot}(V_g)\neq \e_F$], which should have G=0, shows instead a conductance $e^2/2h$ over a wide range of $V_g$, due to this leaked mode into the dot. Interestingly, this pinning effect only occurs when the dot level is coupled to a Majorana mode; ordinary fermionic modes in the wire simply split and broaden (if a continuum) the dot level. We discuss three experimental scenarios to probe the Majorana modes in wires via these leaked/pinned dot modes.

Ballistic spin resonance was experimentally observed in a quasi-one-dimensional wire by Frolov et al. [Nature (London) 458, 868 (2009)]. The spin resonance was generated by a combination of an external static magnetic field and the oscillating effective spin-orbit magnetic field due to periodic bouncings of the electrons off the boundaries of a narrow channel. An increase of the D'yakonov-Perel spin relaxation rate was observed when the frequency of the spin-orbit field matched that of the Larmor precession frequency around the external magnetic field. Here we develop a model to account for the D'yakonov-Perel mechanism in multisubband quantum wires with both the Rashba and Dresselhaus spin-orbit interactions. Considering elastic spin-conserving impurity scatterings in the time-evolution operator (Heisenberg representation), we extract the spin relaxation time by evaluating the time dependent average of the spin operators. The magnetic field dependence of the non-local voltage, which is related to the spin relaxation time behavior, shows a wide plateau, in agreement with the experimental observation. This plateau arises due to injection in higher subbands and small-angle scattering. In this quantum mechanical approach, the spin resonance occurs near the spin-orbit induced energy anticrossings of the quantum wire subbands with opposite spins. We also predict anomalous dips in the spin relaxation time as a function of the magnetic field in systems with strong spin-orbit couplings.

We investigate the spin relaxation and decoherence in a single-electron graphene quantum dot with Rashba and intrinsic spin-orbit interactions. We derive an effective spin-phonon Hamiltonian via the Schrieffer-Wolff transformation in order to calculate the spin relaxation time T_1 and decoherence time T_2 within the framework of the Bloch-Redfield theory. In this model, the emergence of a non-monotonic dependence of T_1 on the external magnetic field is attributed to the Rashba spin-orbit coupling-induced anticrossing of opposite spin states. A rapid decrease of T_1 occurs when the spin and orbital relaxation rates become comparable in the vicinity of the spin-mixing energy-level anticrossing. By contrast, the intrinsic spin-orbit interaction leads to a monotonic magnetic field dependence of the spin relaxation rate which is caused solely by the direct spin-phonon coupling mechanism. Within our model, we demonstrate that the decoherence time T_2 ~ 2 T_1 is dominated by relaxation processes for the electron-phonon coupling mechanisms in graphene up to leading order in the spin-orbit interaction. Moreover, we show that the energy anticrossing also leads to a vanishing pure spin dephasing rate for these states for a super-Ohmic bath.

We theoretically investigate the local density of states (LDOS) probed by a STM tip of ferromagnetic metals hosting a single adatom and a subsurface impurity. We model the system via the two-impurity Anderson Hamiltonian. By using the equation of motion with the relevant Green functions, we derive analytical expressions for the LDOS of two host types: a surface and a quantum wire. The LDOS reveals Friedel-like oscillations and Fano interference as a function of the STM tip position. These oscillations strongly depend on the host dimension. Interestingly, we find that the spin-dependent Fermi wave numbers of the hosts give rise to spin-polarized quantum beats in the LDOS. While the LDOS for the metallic surface shows a damped beating pattern, it exhibits an opposite behavior in the quantum wire. Due to this absence of damping, the wire operates as a spatially resolved spin filter with a high efficiency.

The two-dimensional topological insulating phase has been experimentally discovered in HgTe quantum wells (QWs). The low-energy physics of two-dimensional topological insulators (TIs) is described by the Bernevig-Hughes-Zhang (BHZ) model, where the realization of a topological or a normal insulating phase depends on the Dirac mass being negative or positive, respectively. We solve the BHZ model for a mass domain configuration, analyzing the effects on the edge modes of a finite Dirac mass in the normal insulating region (soft-wall boundary condition). We show that at a boundary between a TI and a normal insulator (NI), the Dirac point of the edge states appearing at the interface strongly depends on the ratio between the Dirac masses in the two regions. We also consider the case of multiple boundaries such as NI/TI/NI, TI/NI/TI and NI/TI/NI/TI.

In this work we study the effects of a longitudinal periodic potential on a parabolic quantum wire defined in a two-dimensional electron gas with Rashba spin-orbit interaction. For an infinite wire superlattice we find, by direct diagonalization, that the energy gaps are shifted away from the usual Bragg planes due to the Rashba spin-orbit interaction. Interestingly, our results show that the location of the band gaps in energy can be controlled via the strength of the Rashba spin-orbit interaction. We have also calculated the charge conductance through a periodic potential of a finite length via the non-equilibrium Green's function method combined with the Landauer formalism. We find dips in the conductance that correspond well to the energy gaps of the infinite wire superlattice. From the infinite wire energy dispersion, we derive an equation relating the location of the conductance dips as a function of the (gate controllable) Fermi energy to the Rashba spin-orbit coupling strength. We propose that the strength of the Rashba spin-orbit interaction can be extracted via a charge conductance measurement.

We theoretically investigate spin-polarized transport in a system composed of a ferromagnetic Scanning Tunneling Microscope (STM) tip coupled to an adsorbed atom (adatom) on a host surface. Electrons can tunnel directly from the tip to the surface or via the adatom. Since the tip is ferromagnetic and the host surface (metal or semiconductor) is non-magnetic we obtain a spin-diode effect when the adatom is in the regime of single occupancy. This effect leads to an unpolarized current for direct bias (V > 0) and polarized current for reverse (V < 0) bias voltages, if the tip is nearby the adatom. Within the nonequilibrium Keldysh technique we analyze the interplay between the lateral displacement of the tip and the intra adatom Coulomb interaction on the spindiode effect. As the tip moves away from the adatom the spin-diode effect vanishes and the currents become polarized for both V > 0 and V < 0. We also find an imbalance between the up and down spin populations in the adatom, which can be tuned by the tip position and the bias. Finally, due to the presence of the adsorbate on the surface, we observe spin-resolved Friedel oscillations in the current, which reflects the oscillations in the calculated LDOS of the subsystem surface+adatom.

We theoretically investigate negative differential resistance (NDR) for ballistic transport in semiconducting armchair graphene nanoribbon (aGNR) superlattices (5 to 20 barriers) at low bias voltages V_SD < 500 mV. We combine the graphene Dirac hamiltonian with the Landauer-Büttiker formalism to calculate the current I_SD through the system. We find three distinct transport regimes in which NDR occurs: (i) a "classical" regime for wide layers, through which the transport across bandgaps is strongly suppressed, leading to alternating regions of nearly unity and zero transmission probabilities as a function of V_SD due to crossing of bandgaps from different layers. (ii) a quantum regime dominated by superlattice miniband conduction, with current suppression arising from the misalignment of miniband states with increasing V_SD and (iii) a Wannier-Stark ladder regime with current peaks occurring at the crossings of Wannier-Stark rungs from distinct ladders. We observe NDR at voltage biases as low as 10 mV with a high current density, making the aGNR superlattices attractive for device applications.

We study the Kondo and transport properties of a quantum dot with a single magnetic Mn ion connected to metallic leads. By employing a numerical renormalization group technique we show that depending on the value of ferromagnetic coupling strength between the local electronic spin and the magnetic moment of the Mn, two distinct Kondo regimes exist. In the weak coupling limit, the system can be found in a completely screened Kondo state describing a local magnetic moment decoupled from the rest of the system. In contrast, in the strong coupling regime the quantum dot spin and the local magnetic moment form a single large-spin entity partially Kondo screened. A crossover between these two regimes can be suitably tuned by varying the tunnel coupling between the quantum dot electron and the leads. The model investigated here is also suitable to study magnetic molecules adsorbed on a metallic surface. The rich phenomenology of these systems is reflected in the conductance across the system.

We introduce an analytical approximation scheme to diagonalize parabolically confined two dimensional electron systems with both the Rashba and Dresselhaus spin-orbit interactions. The starting point of our perturbative expansion is a zeroth-order Hamiltonian for an electron confined in a quantum wire with an effective spin-orbit induced magnetic field along the wire, obtained by properly rotating the usual spin-orbit Hamiltonian. We find that the spin-orbit-related transverse coupling terms can be recast into two parts W and V, which couple crossing and non-crossing adjacent transverse modes, respectively. Interestingly, the zeroth-order Hamiltonian together with W can be solved exactly, as it maps onto the Jaynes-Cummings model of quantum optics. We treat the V coupling by performing a Schrieffer-Wolff transformation. This allows us to obtain an effective Hamiltonian to third order in the coupling strength k_Rl of V, which can be straightforwardly diagonalized via an additional unitary transformation. We also apply our approach to other types of effective parabolic confinement, e.g., 2D electrons in a perpendicular magnetic field. To demonstrate the usefulness of our approximate eigensolutions, we obtain analytical expressions for the n^th Landau-level g_n-factors in the presence of both Rashba and Dresselhaus couplings. For small values of the bulk g-factors, we find that spin-orbit effects cancel out entirely for particular values of the spin-orbit couplings. By solving simple transcendental equations we also obtain the band minima of a Rashba-coupled quantum wire as a function of an external magnetic field. These can be used to describe Shubnikov-de Haas oscillations. This procedure makes it easier to extract the strength of the spin-orbit interaction in these systems via proper fitting of the data.

The longitudinal resistivity ρ_xx of two-dimensional electron gases formed in wells with two subbands displays ringlike structures when plotted in a density--magnetic-field diagram, due to the crossings of spin-split Landau levels (LLs) from distinct subbands. Using spin density functional theory, we investigate the shape and spin polarization of these structures as a function of the temperature and the magnetic-field tilt angle. We find that (i) some of the rings "break" at sufficiently low temperatures due to a quantum Hall ferromagnetic phase transition, thus exhibiting a high degree of spin polarization (∼ 50%) within, consistent with the NMR data of Zhang et al. [Phys. Rev. Lett. 98, 246802 (2007)], and (ii) for increasing tilting angles the interplay between the anticrossings due to inter-LL couplings and the exchange-correlation (XC) effects leads to a collapse of the rings at some critical angle θ_c, in agreement with the data of Guo et al. [Phys. Rev. B 98, 246802 (2008)].

In recent years, spin-related effects have emerged as the key ingredient underlying many fundamental spin-dependent phenomena in nanoscale condensed-matter systems. In this context, the 5th International Conference on Physics and Applications of Spin-related Phenomena in Semiconductors (PASPS V) took place in the city of Foz do Iguaçu, Brazil, on August 3-6, 2008. PASPS V followed the successful series of conferences held in Japan (Sendai, 2000, 2006), Germany (Wurzburg, 2002), and The United States (Santa Barbara, 2004).

In the quantum Hall regime, the longitudinal resistivity \rho_xx plotted as a density-magnetic-field (n_2D-B) diagram displays ringlike structures due to the crossings of two sets of spin split Landau levels from different subbands [see, e.g., Zhang et al., in Phys. Rev. Lett. 95:216801, 2005. For tilted magnetic fields, some of these ringlike structures 'shrink' as the tilt angle is increased and fully collapse at \theta_c ~ 6 degrees. Here we theoretically investigate the topology of these structures via a non-interacting model for the 2DEG. We account for the inter Landau-level coupling induced by the tilted magnetic field via perturbation theory. This coupling results in anticrossings of Landau levels with parallel spins. With the new energy spectrum, we calculate the corresponding n_2D - B diagram of the density of states (DOS) near the Fermi level. We argue that the DOS displays the same topology as \rho_xx in the n_2D - B diagram. For the ring with filling factor \nu = 4, we find that the anticrossings make it shrink for increasing tilt angles and collapse at a large enough angle. Using effective parameters to fit the theta=0 data, we find a collapsing angle \theta_c ~ 3.6 degrees. Despite this factor-of-two discrepancy with the experimental data, our model captures the essential mechanism underlying the ring collapse.

We investigate the spin Hall conductivity \sigma_xy^z of a clean 2D electron gas formed in a two-subband well. We determine \sigma_xy^z as arising from the inter-subband induced spin-orbit (SO) coupling \eta (Calsaverini et al., Phys. Rev. B 78:155313, 2008) via a linear-response approach due to Rashba. By self-consistently calculating η for realistic wells, we find that \sigma_xy^z presents a non-monotonic (and non-universal) behavior and a sign change as the Fermi energy varies between the subband edges. Although our σ xy z is very small (i.e., < < e/4Pi), it is non-zero as opposed to linear-in-k SO models.

We apply the master equation technique to calculate shot noise in a system composed of single level quantum dot attached to a normal metal lead and to a ferromagnetic lead (NM-QD-FM). It is known that this system operates as a spin-diode, giving unpolarized currents for forward bias and polarized current for reverse bias. This effect is observed when only one electron can tunnel at a time through the dot, due to the strong intradot Coulomb interaction. We find that the shot noise also presents a signature of this spin-diode effect, with a super-Poissonian shot noise for forward and a sub-Poissonian shot noise for reverse bias voltages. The shot noise thus can provide further experimental evidence of the spin-rectification in the NM-QD-FM geometry.

We investigate the intrinsic spin Hall effect in two-dimensional electron gases in quantum wells with two subbands, where a new intersubband-induced spin-orbit coupling is operative. The bulk spin Hall conductivity $\sigma_xy^z$ is calculated in the ballistic limit within the standard Kubo formalism in the presence of a magnetic field $B$ and is found to remain finite in the B=0 limit, as long as only the lowest subband is occupied. Our calculated $\sigma_xy^z$ exhibits a non-monotonic behavior and can change its sign as the Fermi energy (the carrier areal density $n_2D$) is varied between the subband edges. We determine the magnitude of $\sigma_xy^z$ for realistic InSb quantum wells by performing a self-consistent calculation of the intersubband-induced spin-orbit coupling.

Recently, we have found an additional spin-orbit (SO) interaction in quantum wells with two subbands [Phys. Rev. Lett. 99, 076603 (2007)]. This new SO term is non-zero even in symmetric geometries, as it arises from the intersubband coupling between confined states of distinct parities, and its strength is comparable to that of the ordinary Rashba. Starting from the $8 \times 8$ Kane model, here we present a detailed derivation of this new SO Hamiltonian and the corresponding SO coupling. In addition, within the self-consistent Hartree approximation, we calculate the strength of this new SO coupling for realistic symmetric modulation-doped wells with two subbands. We consider gated structures with either a constant areal electron density or a constant chemical potential. In the parameter range studied, both models give similar results. By considering the effects of an external applied bias, which breaks the structural inversion symmetry of the wells, we also calculate the strength of the resulting induced Rashba couplings within each subband. Interestingly, we find that for double wells the Rashba couplings for the first and second subbands interchange signs abruptly across the zero bias, while the intersubband SO coupling exhibits a resonant behavior near this symmetric configuration. For completeness we also determine the strength of the Dresselhaus couplings and find them essentially constant as function of the applied bias.

We study spin polarization induced by an applied bias in a bilayer quantum well system with interlayer spin-orbit coupling. The bias is incorporated via the non-equilibrium Green's function formalism, which allows us to handle a variety of system configurations. We shall focus on the component of the spin density perpendicular to the bilayer and compare our results to those obtained for a single layer system.

Using non-equilibrium Green functions we calculate the spin-polarized current and shot noise in a ferromagnet--quantum-dot--ferromagnet (FM-QD-FM) system. Both parallel (P) and antiparallel (AP) magnetic configurations are considered. Coulomb interaction and spin-flip are taken into account within the dot. We find that the interplay between Coulomb interaction and spin accumulation in the dot can result in a bias-dependent current polarization $\wp$. In particular, $\wp$ can be suppressed in the P alignment and enhanced in the AP case depending on the bias voltage. The spin-flip can also result in a switch of the current polarization from the emitter to the collector lead. Interestingly, for a particular set of parameters it is possible to have a polarized current in the collector and an unpolarized current in the emitter lead. We also found a suppression of the Fano factor to values well below 0.5 due to spin-flip.

A general approach to the measurement of an observable with pre- and post-sel​ection is presented. The limit of weak measurement is studied in detail, and it is shown that the phase of the probe, including a Hamiltonian contribution to it, gives rise to observable effects, since the coherence of the probe is essential for the concept of complex weak value to be meaningful. As a particular example, the measurement of a spin component is considered. We find that the contribution of the imaginary part of the weak value is sizeable in this case.

Recently, we have introduced a novel inter-subband-induced spin-orbit (s-o) coupling (Phys. Rev. Lett. 99, 076603 (2007); cond-mat/0607218) arising in symmetric wells with at least two subbands. This new s-o coupling gives rise to an usual zitterbewegung -- i.e. the semiconductor analog to the relativistic trembling motion of electrons -- with cycloidal motion without magnetic fields. Here we complement these findings by explicitly deriving expressions for the corresponding zitterbewegung in spin space.

Using canonical transformations we diagonalize approximately the Hamiltonian of a gaussian wire with Rashba spin-orbit interaction. This proceedure allows us to obtain the energy dispersion relations and the wavefunctions with good accuracy, even in systems with relatively strong Rashba coupling. With these eigenstates one can calculate the non-equilibrium spin densities induced by applying bias voltages across the sample. We focus on the $z$-component of the spin density, which is related to the spin Hall effect.

We report a study of spin dependent transport in a system composed of a quantum dot coupled to a normal metal lead and a ferromagnetic lead (NM-QD-FM). We use the master equation approach to calculate the spin-resolved currents in the presence of an external bias and an intra-dot Coulomb interaction. We find that for a range of positive external biases (current flow from the normal metal to the ferromagnet) the current polarization $\wp=(I_\uparrow-I_\downarrow)/(I_\uparrow+I_\downarrow)$ is suppressed to zero, while for the corresponding negative biases (current flow from the ferromagnet to the normal metal) $\wp$ attains a relative maximum value. The system thus operates as a rectifier for spin--current polarization. This effect follows from an interplay between Coulomb blockade and nonequilibrium spin accumulation in the dot. In the parameter range considered, we also show that the above results can be obtained via nonequilibrium Green functions within a Hartree-Fock type approximation.

Motivated by recent experiments [Zhang \textit{et al.}, Phys. Rev. Lett. \textbf{95}, 216801 (2005) and Ellenberger \textit{et al.}, cond-mat/0602271] reporting novel ringlike structures in the density--magnetic-field ($n_2D$\emph{--B}) diagrams of the longitudinal resistivity $\rho_xx$ of quantum wells with two subbands, we investigate theoretically here the magneto-transport properties of these quantum-Hall systems. We determine $\rho_xx$ via both the Hartree and the Kohn-Sham self-consistent schemes plus the Kubo formula. While the Hartree calculation yields diamond-shaped structures in the $n_2D$\emph{--B} diagram, the calculation including exchange and correlation effects (Kohn-Sham) more closely reproduces the ringlike structures in the experiments.

We investigate the spin-orbit (s-o) interaction in two-dimensional electron gases (2DEGs) in quantum wells with two subbands. From the $8\times 8$ Kane model, we derive a new inter-subband-induced s-o term which resembles the functional form of the Rashba s-o -- but is non-zero even in \emph{symmetric} structures. This follows from the distinct parity of the confined states (even/odd) which obliterates the need for asymmetric potentials. We self-consistently calculate the new s-o coupling strength for realistic wells and find it comparable to the usual Rashba constant. Our new s-o term gives rise to a non-zero ballistic spin-Hall conductivity, which changes sign as a function of the Fermi energy ($\varepsilon_F$), and can induce an unusual \emph{zitterbewegung} with cycloidal trajectories \textit{without} magnetic fields.

In this review we discuss a recent proposal to perform partial Bell-state (parity) measurements on two-electron spin states for electrons confined to quantum dots. The realization of this proposal would allow for a physical implementation of measurement-based quantum computing. In addition, we consider the primary sources of energy relaxation and decoherence which provide the ultimate limit to all proposals for quantum information processing using electron spins in quantum dots. We give an account of the Hamiltonians used for the most important interactions (spin-orbit and hyperfine) and survey some of the recent work done to understand dynamics, control, and decoherence under the action of these Hamiltonians. We conclude the review with a table of important decay times found in experiment, and relate these time scales to the potential viability of measurement-based quantum computing.

We extend our previous work on shot noise for entangled and spin polarized electrons in a beam-splitter geometry with spin-orbit (\textit{s-o}) interaction in one of the incoming leads (lead 1). Besides accounting for both the Dresselhaus and the Rashba spin-orbit terms, we present general formulas for the shot noise of singlet and triplets states derived within the scattering approach. We determine the full scattering matrix of the system for the case of leads with \textit{two} orbital channels coupled via weak \textit{s-o} interactions inducing channel anticrossings. We show that this interband coupling coherently transfers electrons between the channels and gives rise to an additional modulation angle -- dependent on both the Rashba and Dresselhaus interaction strengths -- which allows for further independent coherent control of the electrons traversing the incoming leads. We derive explicit shot noise formulas for a variety of correlated pairs (e.g., Bell states) and lead spin polarizations. Interestingly, the singlet and \textit{each} of the triplets defined along the quantization axis perpendicular to lead 1 (with the local \textit{s-o} interaction) and in the plane of the beam splitter display distinctive shot noise for injection energies near the channel anticrossings; hence, one can tell apart all the triplets, in addition to the singlet, through noise measurements. We also find that spin-orbit induced backscattering within lead 1 reduces the visibility of the noise oscillations, due to the additional partition noise in this lead. Finally, we consider injection of two-particle wavepackets into leads with multiple discrete states and find that two-particle entanglement can still be observed via noise bunching and antibunching.

Editorial summary. Electrons not only have mass and charge, they also have magnetic properties directly related to their intrinsic spin. These spins can combine into quantum states of different spin parity, and such states may be useful as qubits in future quantum computers. As Egues discusses in his Perspective, Engel and Loss [ Science 309, 586 (2005)] report in this issue a method for "fingerprinting" the spin states of electrons contained in quantum dot structures. By allowing the electrons to leak from one dot to another, and then using a nanowire to sense the presence of the spin states, the authors were able to perform a nondestructive spin-parity measurement. Such a spin-parity detector should permit the manipulation of quantum dot qubits for quantum computation.

We have reconsidered the relevant problem of spin injection across ferromagnet/non-magnetic-semiconductor (FM/NMS) and dilute-magnetic-semiconductor/non-magnetic-semiconductor interfaces, for structures with \textit{finite} magnetic layers (FM or DMS). By using appropriate physical boundary conditions, we find new expressions for the resistances of these structures which are in general different from previous results in the literature. The results obtained can be important for the interpretation of the experimental data in the case of DMS/NMS structures.

We use spin-density-functional theory to study recently reported hysteretic magnetoresistance $\rho_xx$ spikes in Mn-based 2D electron gases [Jaroszy\'{n}ski \textit{et al.} Phys. Rev. Lett. \textbf{89}, 266802 (2002)]. We find hysteresis loops in our calculated Landau fan diagrams and total energies signaling quantum-Hall-ferromagnet phase transitions. Spin-dependent exchange-correlation effects are crucial to stabilize the relevant magnetic phases arising from \emph{distinct}symmetry-broken excited- and ground-state solutions of the Kohn-Sham equations. Besides hysteretic spikes in $\rho _xx$, we predict \textit{hysteretic dips} in the Hall resistance $ \rho _xy$. Our theory, \textit{without} domain walls, satisfactorily explains the recent data.

In this paper we theoretically investigate the magnetic-field and temperature dependences of the Shubnikov-de Haas oscillations in group II-VI modulation-doped Digital Magnetic Heterostructures. We self-consistently solve the effective-mass Schroedinger equation within the Hartree approximation and calculate the electronic structure and the magneto-transport properties. Our results show i) a shift of the Shubnikov-de Haas minima to lower magnetic fields with increasing temperature, and ii) an anomalous oscillation which develops when two opposite Landau levels cross near the Fermi energy. Both of these are consistent with recent magneto-transport measurements in such heterostructures [R. Knobel et al., Phys. Rev. B 65, 235327 (2002)].

Using the Keldysh nonequilibrium technique, we study current and the tunnelling magnetoresistance (TMR) in a quantum dot coupled to two ferromagnetic leads (FM-dot-FM). The current is calculated for both parallel and antiparallel lead alignments. Coulomb interaction and spin-flip scattering are taken into account within the quantum dot. Interestingly, we find that these interactions play a contrasting role in the TMR: there is a parameter range where spin flip suppresses the TMR, while Coulomb correlations enhance it, due to Coulomb blockade.

We review our recent work towards quantum communication in a solid-state environment with qubits carried by electron spins. We propose three schemes to produce spin-entangled electrons, where the required separation of the partner electrons is achieved via Coulomb interaction. The non-product spin-states originate either from the Cooper pairs found in a superconductor, or in the ground state of a quantum dot with an even number of electrons. In a second stage, we show how spin-entanglement carried by a singlet can be detected in a beam-splitter geometry by an increased (bunching) or decreased (antibunching) noise signal. We also discuss how a local spin-orbit interaction can be used to provide a continuous modulation of the noise as a signature of entanglement. Finally, we review how one can use a quantum dot as a spin- lter, a spin-memory read-out, a probe for single-spin decoherence and ultimately, a single-spin measurement apparatus.

Digital magnetic heterostructures (DMH) are semiconductor structures with magnetic monolayers. Here we study electronic and magnetotransport properties of shallow modulation-doped (ZnSe/ZnCdSe) DMHs with spin-5/2 Mn impurities. We compare the 'reservoir' model, possibly relevant to shallow geometries, to the usual 'constant-density' model. Our results are obtained by solving the Kohn-Sham equations within the local spin density approximation (LSDA). In the presence of a magnetic field, we show that both models exhibit characteristic behaviors for the electronic structure, two-dimensional carrier density, Fermi level and transport properties. Our results illustrate the relevance of exchange and correlation effects in the study of shallow heterostructures of the group II-VI.

An electronic beam splitter with a local Rashba spin-orbit coupling can serve as a detector for spin-polarized currents. The spin-orbit coupling plays the role of a tunable spin rotator and can be controlled via a gate electrode on top of the conductor. We use spin-resolved scattering theory to calculate the zero-temperature current fluctuations (shot noise) for such a four-terminal device and show that the shot noise is proportional to the spin polarization of the source. Moreover, we analyze the effect of spin-orbit-induced intersubband coupling, leading to an additional spin rotation.

We propose a spin field-effect transistor based on spin-orbit (s-o) coupling of both the Rashba and the Dresselhaus types. Differently from earlier proposals, spin transport through our device is tolerant against spin-independent scattering processes. Hence the requirement of strictly ballistic transport can be relaxed. This follows from a unique interplay between the Dresselhaus and the (gate-controlled) Rashba interactions; these can be tuned to have equal strengths thus yielding k-independent eigenspinors even in two dimensions. We discuss implementations with two-dimensional devices and quantum wires. In the latter, our setup presents strictly parabolic dispersions which avoids complications arising from anticrossings of different bands.

We review our recent contributions on shot noise for entangled electrons and spin-polarized currents in novel mesoscopic geometries. We first discuss some of our recent proposals for electron entanglers involving a superconductor coupled to a double dot in the Coulomb blockade regime, a superconductor tunnel-coupled to Luttinger-liquid leads, and a triple-dot setup coupled to Fermi leads. We calculate current and shot noise for spin-polarized currents and entangled/unentangled electron pairs in a beam-splitter geometry with a \textit{local} Rashba spin-orbit (s-o) interaction in the incoming leads. We find \textit{continuous} bunching and antibunching behaviors for the \textit{entangled} pairs -- triplet and singlet -- as a function of the Rashba rotation angle. In addition, we find that unentangled triplets and the entangled one exhibit distinct shot noise. Shot noise for spin-polarized currents shows sizable oscillations as a function of the Rashba phase. This happens only for electrons injected perpendicular to the Rashba rotation axis; spin-polarized carriers along the Rashba axis are noiseless. We find an additional spin rotation for electrons with energies near the crossing of the bands where s-o induced interband coupling is relevant. This gives rise to an additional modulation of the noise for both electron pairs and spin-polarized currents. Finally, we briefly discuss shot noise for a double dot near the Kondo regime.

We consider a two-channel spin transistor with weak spin-orbit induced interband coupling. We show that the coherent transfer of carriers between the coupled channels gives rise to an \textit{additional} spin rotation. We calculate the corresponding spin-resolved current in a Datta-Das geometry and show that a weak interband mixing leads to enhanced spin control.

Using the Keldysh nonequilibrium technique we calculate current, noise and Fano factor in a ferromagnetic(FM)-quantum dot-ferromagnetic(FM) system with Coulomb interaction and spin-flip scattering in the dot. The lead polarizations are considered in both parallel P and antiparallel AP alignments. We show that spin-flip can increase both AP-current and AP-noise, while the P-current and P-noise are almost insensitive to it. This fact leads to a suppression of the tunnelling magnetoresistance with increasing spin-flip rate.

We have recently calculated shot noise for entangled and spin-polarized electrons in novel beam-splitter geometries with a local Rashba s-o interaction in the incoming leads. This interaction allows for a gate-controlled rotation of the incoming electron spins. Here we present an alternate simpler route to the shot noise calculation in the above work and focus on only electron pairs. Shot noise for these shows continuous bunching and antibunching behaviors. In addition, entangled and unentangled triplets yield distinctive shot noise oscillations. Besides allowing for a direct way to identify triplet and singlet states, these oscillations can be used to extract s-o coupling constants through noise measurements. Incoming leads with spin-orbit interband mixing give rise an additional modulation of the current noise. This extra rotation allows the design of a spin transistor with enhanced spin control.

We investigate the nu=1 quantum Hall ferromagnet in the presence of spin-orbit coupling of the Rashba or Dresselhaus type by means of Hartree-Fock-typed variational states. In the presence of Rashba (Dresselhaus) spin-orbit coupling the fully spin-polarized quantum Hall state is always unstable resulting in a reduction of the spin polarization if the product of the particle charge $q$ and the effective $g$-factor is positive (negative). In all other cases an alternative variational state with O(2) symmetry and finite in-plane spin components is lower in energy than the fully spin-polarized state for large enough spin-orbit interaction. The phase diagram resulting from these considerations differs qualitatively from earlier studies.

We study shot noise for spin-polarized currents and entangled electron pairs in a four-probe (beam splitter) geometry with a local Rashba spin-orbit (s-o) interaction in the incoming leads. Within the scattering formalism we find that shot noise exhibits Rashba-induced oscillations with continuous bunching and antibunching. We show that entangled states as well as triplet states can be identified via their Rashba phase in noise measurements. For two-channel leads we find an additional spin rotation due to s-o induced interband coupling which provides additional spin control. We show that the s-o interaction determines the Fano factor which provides a direct way to measure the Rashba coupling constant via noise.

We study conductance and spin-polarization fluctuations in one-dimensional wires with spin-5/2 magnetic impurities. Our tight-binding Green function approach goes beyond mean field thus including s-d exchange-induced spin-flip scattering exactly. In a certain parameter range, we find that spin flip suppresses conductance fluctuations while enhancing spin-polarization fluctuations. More importantly, spin-polarization fluctuations attain a universal value 1/3 for large enough spin flip strengths.

Within a hydrodynamic approach we investigate the dynamics of an inhomogeneous electron-hole gas coupled to phonons in Te and the corresponding THz emission. We find that the {\em longitudinal} {\em % inhomogeneity} of the photogenerated electron-hole gas -- due to short absorption lengths in Te -- gives rise to {\em screening ineffectiveness} for non-zero wave-vector modes. This allows for THz dynamics and emission at the bare LO phonon frequency $\nu _LO$ even at high carrier densities. Screening ineffectiveness thus provides an appealingly simple explanation for the existence of bare modes at $\nu _LO$ in longitudinally inhomogeneous systems such as Te; no lateral inhomogeneity of the excitation spot is needed here.

We present a normal-mode analysis of coupled photocarrier-phonon dynamics in Te. We consider a dielectric function which accounts for LO phonons and the electron-hole gas within the Debye-Huckel model and RPA. Our main finding is the existence of a bare LO phonon mode in the system even at high carrier density. This oscillation is an unscreened L- mode arising from ineffective screening at large wave vectors. This mode is consistent with the bare LO-phonon peak in recent THz-emission spectra of Te.

Here we investigate the spin-dependent subband structure of newly-developed Mn-based modulation-doped quantum wells. In the presence of an external magnetic field, the s-d exchange coupling between carriers and localized d electrons of the Mn impurities gives rise to large spin splittings resulting in a magnetic-field dependent subband structure. Within the framework of the effective-mass approximation, we self-consistently calculate the subband structure at zero temperature using Density Functional Theory (DFT) with a Local Spin Density Approximation (LSDA). We present results for the magnetic-field dependence of the subband structure of shallow ZnSe/ZnCdMnSe modulation doped quantum wells. Our results show a significant contribution to the self-consistent potential due to the exchange-correlation term. These calculations are the first step in the study of a variety of interesting spin-dependent phenomena, e.g., spin-resolved transport and many-body effects in polarized two-dimensional electron gases.

Shot noise is a time-dependent current fluctuation due to the discrete character of the electron charge. Here we investigate shot noise in a spin-resolved tunneling system under the influence of spin-flip scattering. We find that the average current $\langle I\rangle $ and Fano factor $\gamma $ (``normalized noise'') present contrasting behavior for differing spin-flip time ratios: $\langle I\rangle $\ decreases while $\gamma $\increases for $\tau_{{\uparrow }{\downarrow }}>\tau_{{\downarrow }{\uparrow }}$\ as compared to the $\tau _{{\uparrow }{\downarrow }}=\tau_{{\downarrow }{\uparrow }}$ case and vice versa for $\tau_{{\uparrow }{\downarrow }}<\tau_{{\downarrow }{\uparrow}}$.

We theoretically investigate magnetoresistance (MR) effects in connection with spin filtering in quantum-coherent transport through tunnel junctions based on non-magnetic/semimagnetic heterostructures. We find that spin filtering in conjunction with the suppression/enhancement of the spin-dependent Fermi seas in semimagnetic contacts gives rise to (i) spin-split kinks in the MR of single barriers and (ii) a robust beating pattern in the MR of double barriers with a semimagnetic well. We believe these are unique signatures for quantum filtering.

We investigate spin-dependent fluctuations in spin-polarized electronic currents in a semimagnetic double-barrier tunneling structure. We use both quantum-coherent and semiclassical approaches to study the effects of spin-flip scattering on shot noise. In a limited parameter range, we find that for a fully spin-polarized incoming beam both descriptions yield shot-noise suppression.

We investigate the ultrafast dynamics of an electron-hole plasma coupled to phonons in bulk GaAs excited with femtosecond laser pulses. Our approach is based on balance equations directly derived from the Boltzmann equation within the relaxation-time approximation. Poisson's equation together with a phenomenological driven-harmonic-oscillator equation supplements our description by accounting for time-dependent electric and vibrational fields. Our calculated internal fields show oscillations at frequencies characteristic of those of coupled plasmon-phonon modes. Our results are consistent with recent experimental data.

This work addresses spin-dependent magnetotransport in a band-gap-matched ZnSe/Zn1-xMnxSe heterostructure. In an external magnetic field the paramagnetic layer behaves as a potential well for spin-down electrons and a potential barrier for spin-up ones. My current-density calculation shows a strong suppression of the spin-up component of the current density for increasing magnetic fields; the total current density is dominated by the spin-down component for B > 2 T. This result gives rise to the possibility of devising spin filters relevant for spin-dependent optoelectronics.

Digital-magnetic heterostructures (DMH's), II-VI quantum wells with "planes" of Mn, exhibit strongly spin-dependent physics. We investigate the magnetic-field (B) dependence of exchange-induced energy splittings and spin-flip scattering in DMH's. We find that Mn clustering is relevant to explain the magnitude and the concentration dependence of recently observed splittings. Our calculated electron spin-Rip times show "branching," i.e., tau(sf)(up-->down) decreases and tau(sf)(down-->up) increases with increasing B. This feature, consistent with recent data, is due to the B-field dependence of the available phase space.

We describe an exactly solvable model of a resonant-tunneling diode in which incoherence is introduced by adding a small random phase to the wave function on each round trip between the barriers —a Fabry-Perot picture with dephasing. We find that this form of incoherence broadens and lowers the resonant transmission peak while conserving its area (current conservation), in agreement with previous studies. The autocorrelation function of the transmission coefficient cannot be characterized by a single width but has two energy scales, which we speculate may identify "coherent" and "incoherent" fractions of the current. The shot noise is raised from the suppressed value found for purely coherent transport towards its classical value. This behavior is supported by a picture using wave packets with differing transmission coefficients impinging on a barrier.

Within the sequential tunneling approach we calculate the zero-frequency shot noise for electrons tunneling through a mesoscopic system with internal scattering. This scattering is included by coupling the resonant level to another set of ‘‘internal’’ states. Our results show that the internal scattering has no effect on the noise provided that the internal states are not coupled to the collector. On the other hand, when electrons can hop from the internal states to the collector, the noise is affected. In some cases the zero-frequency noise can be suppressed below one-half of full shot noise, 2eI. All limiting cases for the ratio of noise to the current, S/2eI, are presented and discussed.