Olesia Dmytruk

We study the topological phase diagram of a setup composed of two nanowires with strong Rashba spin-orbit interaction subjected to an external magnetic field and brought into the proximity to a bulk s-wave superconductor in the presence of a supercurrent flowing through it. The supercurrent reduces the critical values of the Zeeman energy and crossed Andreev superconducting pairing required to reach the topological phase characterized by the presence of one Majorana bound state localized at each system end. We demonstrate that, even in the regime of the crossed Andreev pairing being smaller than the direct pairing, a relatively weak magnetic field drives the system into the topological phase due to the presence of the supercurrent.

We study an analytical model of a Rashba nanowire that is partially covered by and coupled to a thin superconducting layer, where the uncovered region of the nanowire forms a quantum dot. We find that, even if there is no topological superconducting phase possible, there is a trivial Andreev bound state that becomes pinned exponentially close to zero energy as a function of magnetic field strength when the length of the quantum dot is tuned with respect to its spin-orbit length such that a resonance condition of Fabry-Perot type is satisfied. In this case, we find that the Andreev bound state remains pinned near zero energy for Zeeman energies that exceed the characteristic spacing between Andreev bound state levels but that are smaller than the spin-orbit energy of the quantum dot. Importantly, as the pinning of the Andreev bound state depends only on properties of the quantum dot, we conclude that this behavior is unrelated to topological superconductivity. To support our analytical model, we also perform a numerical simulation of a hybrid system while explicitly incorporating a thin superconducting layer, showing that all qualitative features of our analytical model are also present in the numerical results.

We study analytically and numerically the renormalization of the g-factor in semiconducting Rashba nanowires (NWs), consisting of a normal and superconducting section. If the potential barrier between the sections is high, a quantum dot (QD) is formed in the normal section. For harmonic (hard-wall) confinement, the effective g-factor of all QD levels is suppressed exponentially (power law) in the product of the spin-orbit interaction (SOI) wave vector and the QD length. If the barrier between the two sections is removed, the g-factor of the emerging Andreev bound states is suppressed less strongly. In the strong SOI regime, and if the chemical potential is tuned to the SOI energy in both sections, the g-factor saturates to a universal constant. Remarkably, the effective g-factor shows a pronounced peak at the SOI energy as function of the chemical potentials. In addition, if the SOI is uniform, the g-factor renormalization as a function of the chemical potential is given by a universal dependence, which is independent of the QD size. This prediction provides a powerful tool to determine experimentally whether the SOI in the whole NW is uniform and, moreover, gives direct access to the SOI strengths of the NW via g-factor measurements. In addition, it allows one to find the optimum position of the chemical potential for bringing the NW into the topological phase at large magnetic fields.

We study both analytically and numerically the role of orbital effects caused by a magnetic field applied along the axis of a semiconducting Rashba nanowire in the topological regime hosting Majorana fermions. We demonstrate that the orbital effects can be effectively taken into account in a one-dimensional model by shifting the chemical potential and thus modifying the topological criterion. We focus on the energy splitting between two Majorana fermions in a finite nanowire and find a striking interplay between orbital and Zeeman effects on this splitting. In the limit of strong spin-orbit interaction, we find regimes where the amplitude of the oscillating splitting stays constant or even decays with increasing the magnetic field, in stark contrast to the commonly studied case where orbital effects of the magnetic field are neglected. The period of these oscillations is found to be almost constant in many parameter regimes.

We theoretically study a Josephson junction based on a semiconducting nanowire subject to a time-dependent flux bias. We establish a general density-matrix approach for the dynamical response of the Majorana junction and calculate the resulting flux-dependent susceptibility using both microscopic and effective low-energy descriptions for the nanowire. We find that the diagonal component of the susceptibility, associated with the dynamics of the Majorana state populations, dominates over the standard Kubo contribution for a wide range of experimentally relevant parameters. The diagonal term, explored, in this Rapid Communication, in the context of Majorana physics, allows probing accurately the presence of Majorana bound states in the junction.

We theoretically study a one-dimensional p-wave superconducting mesoscopic ring interrupted by a weak link and coupled inductively to a microwave cavity. We establish an input-output description for the cavity field in the presence of the ring, and identify the electronic contributions to the cavity response and their dependence on various parameters, such as the magnetic flux, chemical potential, and cavity frequency. We show that the cavity response is 4π periodic as a function of the magnetic flux in the topological region, stemming from the so-called fractional Josephson current carried by the Majorana fermions, while it is 2π periodic in the nontopological phase, consistent with the normal Josephson effect. We find a strong dependence of the signal on the cavity frequency, as well as on the parity of the ground state. Our model takes into account fully the interplay between the low-energy Majorana modes and the gapped bulks states, which we show is crucial for visualizing the evolution of the Josephson effect during the transition from the topological to the trivial phase.

We consider a superconducting microwave cavity capacitively coupled to both a quantum conductor and its electronic reservoirs. We analyze in detail how the measurements of the cavity microwave field, which are related to the electronic charge susceptibility, can be used to extract information on the transport properties of the quantum conductor. We show that the asymmetry of the capacitive couplings between the electronic reservoirs and the cavity plays a crucial role in relating optical measurements to transport properties. For asymmetric capacitive couplings, photonic measurements can be used to probe the finite low-frequency admittance of the quantum conductor, the real part of which is related to the differential conductance. In particular, when the quantum dot is far from resonance, the charge susceptibility is directly proportional to the admittance for a large range of frequencies and voltages. However, when the quantum conductor is near resonance, such a relation generally holds only at low frequency and for equal tunnel coupling or low voltage. Beyond this low-energy near-equilibrium regime, the charge susceptibility and thus the optical transmission offer new insights into the quantum conductors since the optical observables are not directly connected to transport quantities. For symmetric lead capacitive couplings, we show that the optical measurements can be used to reveal the Korringa-Shiba relation, connecting the reactive to the dissipative part of the susceptibility, at low frequency and low bias.

We study one-dimensional p-wave superconductors capacitively coupled to a microwave stripline cavity. By probing the light exiting from the cavity, one can reveal the electronic susceptibility of the p-wave superconductor. We analyze two superconducting systems: the prototypical Kitaev chain and a topological semiconducting wire. For both systems, we show that the photonic measurements, via the electronic susceptibility, allow us to determine the topological phase-transition point, the emergence of the Majorana fermions, and the parity of their ground state. We show that all of these effects, which are absent in effective theories that take into account the coupling of light to Majorana fermions only, are due to the interplay between the Majorana fermions and the bulk states of the superconductors.

The peculiarities and the possibility of a control of exciton condensed pulse movement in semiconductor double quantum wells under the slot in the metal electrode are studied. The condensed phase has been considered phenomenologically with the free energy in Landau-Ginzburg form taking into account the finite value of the exciton lifetime. It was shown that the exciton condensed phase pulse moves along the slot driven by an external linear potential. If the exciton density is high enough for the formation of the condensed phase then the pulse moves maintaining a constant value of a maximum density during exciton lifetime, while the exciton gas phase pulse diffuses. The penetration of the exciton condensed phase pulse through a barrier and its stopping by the barrier have been studied. Additionally, it was shown that the exciton pulse in the condensed phase can be amplified and recovered after damping by an additional laser pulse. Solutions for the system of excitons in double quantum wells under the slot in the electrode under steady irradiation in the form of bright and dark autosolitons were found.

Formation and movement of an exciton pulse in an inhomogeneous potential are studied. It is shown that the pulse does not blur and the maximum of the exciton density in the pulse remains constant during the exciton lifetime if the pulse is formed from the condensed phase. The path, traversed by the excitons, can be increased by imposing an additional laser pulse on the system. Thereby, such a system can be used for information transmission over the exciton condensed phase.