Generic helical edge states due to Rashba spin-orbit coupling in a topological insulator

Abstract

We study the helical edge states of a two-dimensional topological insulator without axial spin symmetry due to the Rashba spin-orbit interaction. Lack of axial spin symmetry can lead to so-called generic helical edge states, which have energy-dependent spin orientation. This opens the possibility of inelastic backscattering and thereby nonquantized transport. Here we find analytically the new dispersion relations and the energy dependent spin orientation of the generic helical edge states in the presence of Rashba spin-orbit coupling within the Bernevig-Hughes-Zhang model, for both a single isolated edge and for a finite width ribbon. In the single-edge case, we analytically quantify the energy dependence of the spin orientation, which turns out to be weak for a realistic HgTe quantum well. Nevertheless, finite size effects combined with Rashba spin-orbit coupling result in two avoided crossings in the energy dispersions, where the spin orientation variation of the edge states is very significantly increased for realistic parameters. Finally, our analytical results are found to compare well to a numerical tight-binding regularization of the model.

Deconvolution of Rashba and Dresselhaus spin-orbit coupling by crystal axis dependent measurements of coupled InAs/GaSb quantum wells

“…The Dresselhaus 15 and Rashba 14 SOC terms contribute in different ways to the production of generic helical edge states, making the deconvolution of these two functionally similar parameters of experimental interest. In particular, the k-linear, electron dominated, Rashba term does not contribute to the disruption of the perfect out-of-plane polarisation, although higher order terms dominated by heavy-holes would be significant 13,14 .…”

“…1(a)) into k-dependent spin-states ( Fig. 1(b)), termed generic helical edge states 14,15 . It is worth noting that generic helical edge states are still protected against elastic backscattering, as this would require a 180º spin-flip 14,15 , as in the unperturbed case.…”

“…1(b)), termed generic helical edge states 14,15 . It is worth noting that generic helical edge states are still protected against elastic backscattering, as this would require a 180º spin-flip 14,15 , as in the unperturbed case. Generic helical edge states do potentially, though, provide a perturbation that would enable easier inelastic backscattering processes, hence disrupting the quantised nature of the conductance in the QSHE.…”

Interacting topological edge channels

“…(S12) is in principle allowed (better to say: not forbidden) by symmetry arguments. By that reasoning, we could have postulated it (without the careful derivation presented above) from the start [29,30]. Another way to argue for a finite g s is related to the edge reconstruction mechanism proposed by Wang, Meir, and Gefen [38].…”

Spin-Polarization Control Driven by a Rashba-Type Effect Breaking the Mirror Symmetry in Two-Dimensional Dual Topological Insulators

“…This odd-in-k effective field, i.e., B ef f (k) = − B ef f (−k), preserves the Tr-symmetry and only appears when the mirror symmetry is broken, in the same way that the Rashba effect depends on the inversion symmetry breaking [44,45]. Analogous to the generic helical edge states [46,47], this field changes the direction of the spin polarization, as observed in Fig. 2 and 3.…”