No Arabic abstract
The presence of edges locally breaks the inversion symmetry of heterostructures and gives rise to lateral (edge) spin-orbit coupling (SOC), which, under some conditions, can lead to the formation of helical edge states. If the edge SOC is strong enough, the helical edge states can penetrate the band-gap and be energetically isolated from the bulk-like states. As a result backward scattering is suppressed, dissipationless helical edge channels protected against time-inversion symmetric perturbations emerge, and the system behaves as a 2D topological insulator (TI). However, unlike in previous works on TIs, the mechanism proposed here for the creation of protected helical edge states relies on the strong edge SOC rather than on band inversion.
We report magnetotransport properties of BaZnBi$_{2}$ single crystals. Whereas electronic structure features Dirac states, such states are removed from the Fermi level by spin-orbit coupling (SOC) and consequently electronic transport is dominated by the small hole and electron pockets. Our results are consistent with three dimensional (3D) but also with quasi two dimensional (2D) portions of the Fermi surface. The spin-orbit coupling-induced gap in Dirac states is much larger when compared to isostructural SrMnBi$_{2}$. This suggests that not only long range magnetic order but also mass of the alkaline earth atoms A in ABX$_{2}$ (A = alkaine earth, B = transition metal and X=Bi/Sb) are important for the presence of low-energy states obeying the relativistic Dirac equation at the Fermi surface
The existence of a spin-orbit coupling (SOC) induced by the gradient of the effective mass in low-dimensional heterostructures is revealed. In structurally asymmetric quasi-two-dimensional semiconductor heterostructures the presence of a mass gradient across the interfaces results in a SOC which competes with the SOC created by the electric field in the valence band. However, in graded quantum wells subjected to an external electric field, the mass-gradient induced SOC can be finite even when the electric field in the valence band vanishes.
We study graphene which has both spin-orbit coupling (SOC), taken to be of the Kane-Mele form, and a Zeeman field induced due to proximity to a ferromagnetic material. We show that a zigzag interface of graphene having SOC with its pristine counterpart hosts robust chiral edge modes in spite of the gapless nature of the pristine graphene; such modes do not occur for armchair interfaces. Next we study the change in the local density of states (LDOS) due to the presence of an impurity in graphene with SOC and Zeeman field, and demonstrate that the Fourier transform of the LDOS close to the Dirac points can act as a measure of the strength of the spin-orbit coupling; in addition, for a specific distribution of impurity atoms, the LDOS is controlled by a destructive interference effect of graphene electrons which is a direct consequence of their Dirac nature. Finally, we study transport across junctions which separates spin-orbit coupled graphene with Kane-Mele and Rashba terms from pristine graphene both in the presence and absence of a Zeeman field. We demonstrate that such junctions are generally spin active, namely, they can rotate the spin so that an incident electron which is spin polarized along some direction has a finite probability of being transmitted with the opposite spin. This leads to a finite, electrically controllable, spin current in such graphene junctions. We discuss possible experiments which can probe our theoretical predictions.
We study electronic transport across a helical edge state exposed to a uniform magnetic ({$vec B$}) field over a finite length. We show that this system exhibits Fabry-Perot type resonances in electronic transport. The intrinsic spin anisotropy of the helical edge states allows us to tune these resonances by changing the direction of the {$vec B$} field while keeping its magnitude constant. This is in sharp contrast to the case of non-helical one dimensional electron gases with a parabolic dispersion, where similar resonances do appear in individual spin channels ($uparrow$ and $downarrow$) separately which, however, cannot be tuned by merely changing the direction of the {$vec B$} field. These resonances provide a unique way to probe the helical nature of the theory.
We consider transport properties of a single edge of a two-dimensional topological insulators, in presence of Rashba spin-orbit coupling, driven by two external time-dependent voltages and connected to a thin superconductor. We focus on the case of a train of Lorentzian-shaped pulses, which are known to generate coherent single-electron excitations in two-dimensional electron gas, and prove that they are minimal excitations for charge transport also in helical edge states, even in the presence of spin-orbit interaction. Importantly, these properties of Lorentzian-shaped pulses can be tested computing charge noise generated by the scattering of particles at the thin superconductor. This represents a novel setup where electron quantum optics experiments with helical states can be implemented, with the superconducting contact as an effective beamsplitter. By elaborating on this configuration, we also evaluate charge noise in a collisional Hong-Ou-Mandel configuration, showing that, due to the peculiar effects induced by Rashba interaction, a non-vanishing dip at zero delay appears.