Code based on the Python package Kwant, referring to the supplemental material of the article "Fabry-Pérot resonant vortices and magnetoconductance in topological insulator constrictions with magnetic barriers".
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Article available in Physical Review B and Arxiv: Fabry-Pérot resonant vortices and magnetoconductance in topological insulator constrictions with magnetic barriers
Abstract of the article:
The edge states of two-dimensional time-reversal topological insulators support a perfect helical conductance on wide ribbons due to the absence of backscattering. Here, we study the changes in the transport properties of topological insulator nanoribbons by introducing a constriction along the ribbon. This setup allows the edge states to hybridize, leading to reflections at the ends of the constriction. We find that the electronic states running along one edge can be reflected back along the opposite edge multiple times, giving rise to Fabry-Pérot resonant vortices within the constriction with well-defined conductance peaks. We show that magnetic barriers allow one to manipulate these peaks and obtain significant changes in the system spin-resolved magnetoconductance.
Figure 1) Current density (arrows) and spin σz polarization [red (blue) for spin-up (spin-down)] across the constriction for the n = 1 (left) and n = 2 (right) FPR peaks in Fig. 2 (dashed lines). The spinup and -down channels show vortices rotating in opposite directions due to the helical nature of the TI. (c, f) Adding both spin channels yields linear spin-polarized flow along the edges for both n = 1 and n = 2.
Figure 2) Current density (arrows) and spin σz polarization across two ν = z barriers (shaded regions centered at x = ±2.5). (a–c) In the first G peak in Fig. 6(b) "see the article" for the P configuration, the spin-down (blue) channel is resonant, while the spin-up (red) channel reflects at the barrier, leading to a total current with a net spin-down polarization. (d–f) The second peak in the P configuration has the opposite spin polarization. (g–i) In the AP configuration, the spin-down channel reflects on the second barrier and the resonant vortex forms in the first section of the constriction, while the spin-up resonance occurs in the second half
