Luka Trifunovic

We introduce a system of stacked two-dimensional electron and hole gas layers with Rashba spin orbit interaction and show that the tunnel coupling between the layers induces a strong three- dimensional (3D) topological insulator phase. At each of the two-dimensional bulk boundaries we find the spectrum consisting of a single anistropic Dirac cone, which we show by analytical and numerical calculations. Our setup has a unit-cell consisting of four tunnel coupled Rashba layers and presents a synthetic strong 3D topological insulator and is distinguished by its rather high experimental feasibility.

We demonstrate theoretically that by placing a ferromagnetic particle between a nitrogen-vacancy (NV) magnetometer and a target spin, the magnetometer sensitivity is increased dramatically. Specifically, using materials and techniques already experimentally available, we find that by taking advantage of the ferromagnetic resonance the minimum magnetic moment that can be measured is smaller by four orders of magnitude in comparison to current state-of-the-art magnetometers. As such, our proposed setup is sensitive enough to detect a single nuclear spin at a distance of 30~nm from the surface within less than one second of data acquisition at room temperature. Our proposal opens the door for nanoscale NMR on biological material under ambient conditions.

We study theoretically transport through a semiconducting nanowire (NW) in the presence of Rashba spin orbit interaction, uniform magnetic field, and spatially modulated magnetic field. The system is fully gapped, and the interplay between the spin orbit interaction and the magnetic fields leads to fractionally charged fermion (FF) bound states of Jackiw-Rebbi type at each end of the nanowire. We investigate the transport and noise behavior of a N/NW/N system, where the wire is contacted by two normal leads (N), and we look for possible signatures that could help in the experimental detection of such states. We find that the differential conductance and the shot noise exhibit a sub-gap structure which fully reveals the presence of the FF state. Our predictions can be tested in standard two-terminal measurements through InSb/InAs nanowires.

We propose a mechanism of a long-range coherent interaction between two singlet-triplet qubits dipolarly coupled to a dogbone-shaped ferromagnet. An effective qubit-qubit interaction Hamiltonian is derived and the coupling strength is estimated. Furthermore we derive the effective coupling between two spin-1/2 qubits that are coupled via dipolar interaction to the ferromagnet and that lie at arbitrary positions and deduce the optimal positioning. We consider hybrid systems consisting of spin-1/2 and ST qubits and derive the effective Hamiltonian for this case. We then show that operation times vary between 1MHz and 100MHz and give explicit estimates for GaAs, Silicon, and NV-center based spin qubits. Finally, we explicitly construct the required sequences to implement a CNOT gate. The resulting quantum computing architecture retains all the single qubit gates and measurement aspects of earlier approaches, but allows qubit spacing at distances of order 1$\,\mu$m for two-qubit gates, achievable with current semiconductor technology.

We propose a mechanism of long-range coherent coupling between spins coupled to a ferromagnet by exchnage or dipolar coupling. An effective two-spin interaction Hamiltonian is derived and the coupling strength is estimated. We also discuss mechanisms of decoherence and consider possibilities for gate control of the interaction between neighboring spin-qubits. The resulting quantum computing architecture retains all the single qubit gates and measurement aspects of earlier approaches, but allows qubit spacing at distances of order 1$\,\mu$m for two-qubit gates, achievable with current semiconductor technology. The clock speed depends strongly on the dimensionality of the ferromagnet and is between MHz and GHz.

Motivated by recent experiments searching for Majorana fermions (MFs) in hybrid semiconducting-superconducting nanostructures and by subsequent theoretical interpretations, we consider the so far most realistic model (including disorder) and analyze its transport behavior numerically. In particular, we include in the model superconducting contacts used in the experiments to extract the current. We show that important new features emerge that are absent in simpler models, such as the enhanced visibility of the topological gap for increased spin-orbit interaction. We find oscillations of the zero bias peak as function of magnetic field and explain their origin. Even taking into account all the possible (known) ingredients of the experiments and exploring many parameter regimes for MFs, we are not able to reach a satisfactory agreement with the reported data. Thus, a different physical origin for the observed zero-bias peak cannot be excluded.

We study finite quantum wires and rings in the presence of a charge density wave gap induced by a periodic modulation of the chemical potential. We show that the Tamm-Shockley bound states emerging at the ends of the wire are stable against weak disorder and interactions, for discrete open chains and for continuum systems. The low-energy physics can be mapped onto the Jackiw-Rebbi equations describing massive Dirac fermions and bound end states. We treat interactions via the continuum model and show that they increase the charge gap and further localize the end states. In an Aharonov-Bohm ring with weak link, the bound states give rise to an unusual $4\pi$-peridodicity in the spectrum and persistent current as function of an external flux. The electrons placed in the two localized states on the opposite ends of the wire can interact via exchange interactions and this setup can be used as a double quantum dot hosting spin-qubits.

We study the impact of the long-range spin-triplet proximity effect on the density of states (DOS) in planar SF1F2S Josephson junctions that consist of conventional superconductors (S) connected by two metallic monodomain ferromagnets (F1 and F2) with transparent interfaces. We determine the electronic DOS in F layers and the Josephson current for arbitrary orientation of the magnetizations using the solutions of Eilenberger equations in the clean limit and for a moderate disorder in ferromagnets. We find that fully developed long-range proximity effect can occur in highly asymmetric ferromagnetic bilayer Josephson junctions with orthogonal magnetizations. The effect manifests itself as an enhancement in DOS, and as a dominant second harmonic in the Josephson current-phase relation. Distinctive variation of DOS in ferromagnets with the angle between magnetizations is experimentally observable by tunneling spectroscopy. This can provide an unambiguous signature of the long-range spin-triplet proximity effect.

The electron spin is a natural two-level system that allows a qubit to be encoded. When localized in a gate-defined quantum dot, the electron spin provides a promising platform for a future functional quantum computer. The essential ingredient of any quantum computer is entanglement - for the case of electron-spin qubits considered here - commonly achieved via the exchange interaction. Nevertheless, there is an immense challenge as to how to scale the system up to include many qubits. In this paper, we propose a novel architecture of a large-scale quantum computer based on a realization of long-distance quantum gates between electron spins localized in quantum dots. The crucial ingredients of such a long-distance coupling are floating metallic gates that mediate electrostatic coupling over large distances. We show, both analytically and numerically, that distant electron spins in an array of quantum dots can be coupled selectively, with coupling strengths that are larger than the electron-spin decay and with switching times on the order of nanoseconds.

We study theoretically the Josephson effect and pairing correlations in planar SF1F2S junctions that consist of conventional superconductors (S) connected by two metallic monodomain ferromagnets (F1 and F2) with transparent interfaces. We obtain both spin-singlet and -triplet pair amplitudes and the Josephson current-phase relations for arbitrary orientation of the magnetizations using the self-consistent solutions of Eilenberger equations in the clean limit and for a moderate disorder in ferromagnets. We find that the long-range triplet correlations cannot prevail in symmetric junctions with equal ferromagnetic layers. Surprisingly, the long-range spin-triplet correlations give the dominant second harmonic in the Josephson current-phase relation of highly asymmetric SF1F2S junctions. The effect is robust against moderate disorder and variations in the layers thickness and exchange energy of ferromagnets.

We consider a long superconductor-ferromagnet-superconductor junction with one spin-active region. It is shown that an odd number of Cooper pairs cannot have a long-range propagation when there is only one spin-active region. When the temperature is much lower than the Thouless energy, the coherent transport of two Cooper pairs becomes the dominant process and the superharmonic current-phase relation is obtained ($I\propto\sin2\phi$).

We study the proximity effect in SF'(AF)F'S and SF'(F)F'S planar junctions, where S is a clean conventional (s-wave) superconductor, while F' and middle layers are clean or moderately diffusive ferromagnets. Middle layers consist of two equal ferromagnets with antiparallel (AF) or parallel (F) magnetizations that are not collinear with magnetizations in the neighboring F' layers. We use fully self-consistent numerical solutions of the Eilenberger equations to calculate the superconducting pair amplitudes and the Josephson current for arbitrary thickness of ferromagnetic layers and the angle between in-plane magnetisations. For moderate disorder in ferromagnets the triplet proximity effect is practically the same for AF and F structures, like in the dirty limit. Triplet Josephson current is dominant for $d'\approx\hbar v_F/2h'$, where $d'$ is the F' layer thickness and $h'$ is the exchange energy. Our results are in a qualitative agreement with the recent experimental observations [T. S. Khaire, M. A. Khasawneh, W. P. Pratt, and N. O. Birge, Phys. Rev. Lett. \textbf{104}, 137002 (2010)].