Landau-Stark states and edge-induced Bloch oscillations in topological lattices

TL;DR

This paper investigates how magnetic fields alter Bloch oscillations in topological lattices, revealing edge-induced behaviors and Landau-Stark states that modify particle dynamics.

Contribution

It introduces the role of magnetic fields in modifying Bloch oscillations, highlighting edge effects and Landau-Stark states in topological lattice systems.

Findings

Magnetic field changes standard Bloch oscillations to include edge-induced acceleration.

Landau-Stark states explain the modified particle dynamics.

Edge effects lead to new oscillation patterns in topological lattices.

Abstract

We consider dynamics of a charged particle in a finite along the $x$ direction square lattice in the presence of normal to the lattice plane magnetic field and in-plane electric field aligned with the $y$ axis. For vanishing magnetic field this dynamics would be common Bloch oscillations where the particle oscillates in the $y$ direction with amplitude inverse proportional to the electric field. We show that a non-zero magnetic field crucially modifies this dynamics. Namely, the new Bloch oscillations consist of time intervals where the particle moves with constant velocity in the $x$ direction intermitted by intervals where it is accelerated or decelerated along the lattice edges. The analysis is done in terms of the Landau-Stark states which are eigenstates of a quantum particle in a two-dimensional lattice subject to (real or synthetic) electric and magnetic fields.