Topological aspects of superconductivity in quantum spin-Hall systems (QSHSs) such as thin layers of three-dimensional topological insulators (3D Tis) or two-dimensional Tis are in the focus of current research. We examine hybrid QSHS/superconductor
structures in an external magnetic field and predict a gapless superconducting state with protected edge modes. It originates entirely from the orbital magnetic-field effect caused by the locking of the electron spin to the momentum of the superconducting condensate flow. We show that such spin-momentum locking can generate a giant orbital g-factor of order of several hundreds, allowing one to achieve significant spin polarization in the QSHS in the fields well below the critical field of the superconducting material. We propose a three-terminal setup in which the spin-polarized edge superconductivity can be probed by Andreev reflection, leading to unusual transport characteristics: a non-monotonic excess current and a zero-bias conductance splitting in the absence of the Zeeman interaction.
Spin-orbit (SO) interactions give a spin-dependent correction r_so to the position operator, referred to as the anomalous position operator. We study the contributions of r_so to the spin-Hall effect (SHE) in quasi two-dimensional (2D) semiconductor
quantum wells with strong band structure SO interactions that cause spin precession. The skew scattering and side-jump scattering terms in the SHE vanish, but we identify two additional terms in the SHE, due to r_so, which have not been considered in the literature so far. One term reflects the modification of the spin precession due to the action of the external electric field (the field drives the current in the quantum well), which produces, via r_so, an effective magnetic field perpendicular to the plane of the quantum well. The other term reflects a similar modification of the spin precession due to the action of the electric field created by random impurities, and appears in a careful formulation of the Born approximation. We refer to these two effects collectively as anomalous spin precession and we note that they contribute to the SHE to the first order in the SO coupling constant even though they formally appear to be of second order. In electron systems with weak momentum scattering, the contribution of the anomalous spin precession due to the external electric field equals 1/2 the usual side-jump SHE, while the additional impurity-dependent contribution depends on the form of the band structure SO coupling. For band structure SO linear in wave vector the two additional contributions cancel. For band structure SO cubic in wave vector only the contribution due to external electric field is present, and can be detected through its density dependence. In 2D hole systems both anomalous spin precession contributions vanish identically.
Using a generalized wave matching method we solve the full scattering problem for quantum spin Hall insulator (QSHI) - superconductor (SC) - QSHI junctions. We find that for systems narrow enough so that the bulk states in the SC part couple both edg
es, the crossed Andreev reflection (CAR) is significant and the electron cotunneling (T) and CAR become spatially separated. We study the effectiveness of this separation as a function of the system geometry and the level of doping in the SC. Moreover, we show that the spatial separation of both effects allows for an all-electrical measurement of CAR and T separately in a 5-terminal setup or by using the spin selection of the quantum spin Hall effect in an H-bar structure.
We analyze thermally induced spin and charge transport in HgTe/CdTe quantum wells on the basis of the numerical non-equilibrium Greens function technique in the linear response regime. In the topologically non-trivial regime, we find a clear signatur
e of the gap of the edge states due to their finite overlap from opposite sample boundaries -- both in the charge Seebeck and spin Nernst signal. We are able to fully understand the physical origin of the thermoelectric transport signatures of edge and bulk states based on simple analytical models. Interestingly, we derive that the spin Nernst signal is related to the spin Hall conductance by a Mott-like relation which is exact to all orders in the temperature difference between the warm and the cold reservoir.
Two-dimensional topological insulators are characterized by gapped bulk states and gapless helical edge states, i.e. time-reversal symmetric edge states accommodating a pair of counter-propagating electrons. An external magnetic field breaks the time
-reversal symmetry. What happens to the edge states in this case? In this paper we analyze the edge-state spectrum and longitudinal conductance in a two-dimensional topological insulator subject to a quantizing magnetic field. We show that the helical edge states exist also in this case. The strong magnetic field modifies the group velocities of the counter-propagating channels which are no longer identical. The helical edge states with different group velocities are particularly prone to get coupled via backscattering, which leads to the suppression of the longitudinal edge magnetoconductance.
We present a unified theory of magnetic damping in itinerant electron ferromagnets at order $q^2$ including electron-electron interactions and disorder scattering. We show that the Gilbert damping coefficient can be expressed in terms of the spin con
ductivity, leading to a Matthiessen-type formula in which disorder and interaction contributions are additive. In a weak ferromagnet regime, electron-electron interactions lead to a strong enhancement of the Gilbert damping.
