Two-terminal transport in biased lattices: transition from ballistic to diffusive current

TL;DR

This paper investigates how quantum transport in a biased lattice transitions from ballistic to diffusive regimes as the tilt increases, highlighting the role of Wannier-Stark localization in this crossover.

Contribution

It provides a detailed analysis of the transition from ballistic to diffusive transport in tilted lattices, identifying the critical tilt based on Wannier-Stark localization length.

Findings

Ballistic transport occurs at small chemical potential differences.

Diffusive Esaki-Tsu regime emerges at large tilts.

The crossover point is when Wannier-Stark localization length matches the lattice length.

Abstract

We analyze quantum transport of charged fermionic particles in the tight-binding lattice connecting two particle reservoirs (the leads). If the lead chemical potentials are different they create an electric field which tilts the lattice. We study the effect of this tilt on quantum transport in the presence of weak relaxation/decoherence processes in the lattice. It is shown that the Landauer ballistic transport regime for a weak tilt (small chemical potential difference) changes to the diffusive Esaki-Tsu transport regime for a strong tilt (large chemical potential difference), where the critical tilt for this crossover is determined by the condition that the Wannier-Stark localization length coincides with the lattice length.