One-dimensional lattice with strong spin-orbit interactions (SOI) and Zeeman magnetic field is shown to lead to the formation of a helical charge-density wave (CDW) state near half-filling. Interplay of the magnetic field, SOI constants and the CDW g
ap seems to support Majorana bound states under appropriate value of the external parameters. Explicit calculation of the quasi-particles wave functions supports a formation of the localized zero-energy state, bounded to the sample end-points. Symmetry classification of the system is provided. Relative value of the density of states shows a precise zero-energy peak at the center of the band in the non-trivial topological regime.
Equilibrium spin-current is calculated in a quasi-two-dimensional electron gas with finite thickness under in-plane magnetic field and in the presence of Rashba- and Dresselhaus spin-orbit interactions. The transverse confinement is modeled by means
of a parabolic potential. An orbital effect of the in-plane magnetic field is shown to mix a transverse quantized spin-up state with nearest-neighboring spin-down states. The out-off-plane component of the equilibrium spin current appears to be not zero in the presence of an in-plane magnetic field, provided at least two transverse-quantized levels are filled. In the absence of the magnetic field the obtained results coincide with the well-known results, yielding cubic dependence of the equilibrium spin current on the spin-orbit coupling constants. The persistent spin-current vanishes in the absence of the magnetic field if Rashba- and Dresselhaus spin-orbit coefficients,{alpha} and {beta}, are equal each other. In-plane magnetic field destroys this symmetry, and accumulates a finite spin-current as {alpha} rightarrow {beta}. Magnetic field is shown to change strongly the equilibrium current of the in-plane spin components, and gives new contributions to the cubic-dependent on spin-orbit constants terms. These new terms depend linearly on the spin-orbit constants.
Effects of the spin-orbit interactions on the energy spectrum, Fermi surface and spin dynamics are studied in structural- and bulk-inversion asymmetric quasi-two-dimensional structures with a finite thickness in the presence of a parabolic transverse
confining potential. One-particle quantum mechanical problem in the presence of an in-plane magnetic field is solved numerically exact. Interplay of the spin-orbit interactions, orbital- and Zeeman-effects of the in-plane magnetic field yields a multi-valley subband structure, typical for realization of the Gunn effect. A possible Gunn-effect-mediated spin accumulation is discussed.
Effects of non-magnetic disorder on the critical temperature T_c and on diamagnetism of quasi-one-dimensional superconductors are reported. The energy of Josephson-coupling between wires is considered to be random, which is typical for dirty organic
superconductors. We show that this randomness destroys phase coherence between wires and that T_c vanishes discontinuously at a critical disorder-strength. The parallel and transverse components of the penetration-depth are evaluated. They diverge at different critical temperatures T_c^{(1)} and T_c, which correspond to pair-breaking and phase-coherence breaking respectively. The interplay between disorder and quantum phase fluctuations is shown to result in quantum critical behavior at T=0, which manifests itself as a superconducting-normal metal phase transition of first-order at a critical disorder strength.
