Transport in tight-binding bond percolation models

TL;DR

This paper investigates transport properties in tight-binding quantum percolation models beyond the threshold, revealing how disorder affects conductivity and the applicability of classical models like Drude, using numerical methods based on quantum typicality.

Contribution

It introduces a numerical approach using quantum typicality to analyze transport in disordered tight-binding models beyond the percolation threshold, providing insights into conductivity and classical model applicability.

Findings

Conductivity aligns with simple heuristic predictions.

Transport can be described by a Drude model depending on disorder level.

The Einstein relation holds under certain conditions.

Abstract

Most of the investigations to date on tight-binding, quantum percolation models focused on the quantum percolation threshold, i.e., the analogue to the Anderson transition. It appears to occur if roughly 30% of the hopping terms are actually present. Thus, models in the delocalized regime may still be substantially disordered, hence analyzing their transport properties is a nontrivial task which we pursue in the paper at hand. Using a method based on quantum typicality to numerically perform linear response theory we find that conductivity and mean free paths are in good accord with results from very simple heuristic considerations. Furthermore we find that depending on the percentage of actually present hopping terms, the transport properties may or may not be described by a Drude model. An investigation of the Einstein relation is also presented.