Zitterbewegung and bulk-edge Landau-Zener tunneling in topological insulators

We investigate the ballistic zitterbewegung dynamics and the Landau-Zener tunneling between edge and bulk states of wave packets in two-dimensional topological insulators. In bulk, we use the Ehrenfest theorem to show that an external in-plane electric field not only drifts the packet longitudinally...

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Bibliographic Details
Published in:arXiv.org 2018-10
Main Authors: Ferreira, Gerson J, Maciel, Renan P, Penteado, Poliana H, Egues, J Carlos
Format: Article
Language:English
Subjects:
Electric fields
Time dependence
Topological insulators
Topology
Wave packets
Online Access:Get full text
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Summary:We investigate the ballistic zitterbewegung dynamics and the Landau-Zener tunneling between edge and bulk states of wave packets in two-dimensional topological insulators. In bulk, we use the Ehrenfest theorem to show that an external in-plane electric field not only drifts the packet longitudinally, but also induces a transverse finite side-jump for both trivial and topological regimes. For finite ribbons of width \(W\), we show that the Landau-Zener tunneling between bulk and edge states vanishes for large \(W\) as their electric field-induced coupling decays with \(W^{-3/2}\). This is demonstrated by expanding the time-dependent Schr\"odinger equation in terms of Houston states. Hence we cannot picture the quantum spin Hall states as arising from the zitterbewegung bulk trajectories `leaking' into the edge states, as proposed in Phys. Rev. B 87, 161115 (2013).
ISSN:2331-8422
DOI:10.48550/arxiv.1807.07390