Induced tunneling and localization for a quantum particle in tilted two-dimensional lattices

TL;DR

This paper investigates how a quantum particle in tilted 2D lattices can exhibit free transverse movement due to induced tunneling effects, revealing band collapse phenomena and potential analogies with photon-induced tunneling.

Contribution

It introduces a novel analysis of induced tunneling and localization effects in tilted 2D lattices, highlighting conditions for free transverse motion and band collapse phenomena.

Findings

Particle can move freely perpendicular to static force in certain lattice geometries.

Dispersion relation shows band collapses as a control parameter varies.

Analogy established with photon-induced tunneling in driven 1D lattices.

Abstract

We consider a quantum particle in tilted two-dimensional lattices in the tight-binding approximations. We found that for some lattice geometries and certain orientations of the static force with respect to the lattice primary axes the particle can freely move across the lattice in the direction perpendicular to the vector of the static force. This effect is argued to be analogue of the photon-induced tunneling in driven one-dimensional lattices. The obtained dispersion relation for the transverse motion of the particle draws this analogy further by eventually showing band collapses when a control parameter is varied.