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

Abstract

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 Schrödinger 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).

Topological Landau–Zener nanophotonic circuits

“…1(d)]. Interestingly, how the finite-size effect affects the energy bandgap has been studied in the platform of condensed matter physics, and the coupling strength can be characterized by the Berry connection 41 …”

“…Interestingly, how the finite-size effect affects the energy bandgap has been studied in the platform of condensed matter physics, and the coupling strength can be characterized by the Berry connection. 41 To analyze the evolution of the states around minimum bandgap points, a widely used method is to characterize the band with an approximate two-level model, i.e., the LZ model, 31,39…”

Spin dynamics and persistent currents on a cylindrical surface of topological insulator

“…In the present research work, the expectation values of the spin operators, in particular, ψ|S ϕ H (t)|ψ and ψ|S ρ H (t)|ψ , see figs. 3(a) and (b), respectively, undergo zetterbewegung oscillations, encoding important information about the electron transport in topological materials [31][32][33]. In addition, the precession of the expectation values of all the components of the spin operator is very small, behaving as quasi-conserved quantities in the course of electron dynamics which reflect the robustness of the conducting metallic surface states of TIs.…”

Valley-driven Zitterbewegung in Kekulé-distorted graphene

“…In connection with graphene, the wave packet dynamics and the Zitterbewegung effect was analyzed by Rusin and Zawadski 26 , and later by Maksimova et al 27 , showing that the effect is dependent of the polarization of the sublattice pseudospin relative to the direction of motion. Subsequent studies have used the dynamics of electron wave packets to study the Zitterbewegung of numerous systems, including Weyl semimetals 28 , the dice lattice 29,30 , silicene 31,32 , phosphorene 33 , borophene 34 and topological insulators [35][36][37] . However, the first direct experimental observation of the effect was realized in the realm of atomic condensates by Le Blanc et al 38 , using Bose-Einstein atomic condensates of 87 Rb atoms.…”