Quench Dynamics of Edge States in 2-D Topological Insulator Ribbons

TL;DR

This paper investigates the non-equilibrium dynamics of edge states in a 2D topological insulator ribbon after a sudden quench, revealing collapse and revival phenomena in edge state coherence and spin Hall current.

Contribution

It models edge state dynamics as decoupled qubits coupled to bulk states and uncovers collapse and revival effects in Loschmidt echo and spin Hall current post-quench.

Findings

Pronounced collapse and revival of Loschmidt echo for edge states

Collapse and revival observed in spin Hall current

Persistence of time-averaged spin Hall current

Abstract

We study the dynamics of edge states of the two dimensional BHZ Hamiltonian in a ribbon geometry following a sudden quench to the quantum critical point separating the topological insulator phase from the trivial insulator phase. The effective edge state Hamiltonian is a collection of decoupled qubit-like two-level systems which get coupled to bulk states following the quench. We notice a pronounced collapse and revival of the Loschmidt echo for low-energy edge states illustrating the oscillation of the state between the two edges. We also observe a similar collapse and revival in the spin Hall current carried by these edge states, leading to a persistence of its time-averaged value.