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

Kirensky Institute of Physics - 660036 Krasnoyarsk, Russia and Siberian Federal University - 660041 Krasnoyarsk, Russia

Received: 22 January 2014
Accepted: 12 May 2014

Abstract

We consider the dynamics of a charged particle in a finite along the x-direction square lattice in the presence of a normal to the lattice plane magnetic field and an in-plane electric field aligned with the y-axis. For a vanishing magnetic field this dynamics would be common Bloch oscillations where the particle oscillates in the y-direction with an 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.