Hidden Symmetries of Electronic Transport in a Disordered One-Dimensional Lattice

TL;DR

This paper investigates how correlated impurities in a one-dimensional disordered lattice affect electronic transport, revealing a hidden symmetry in transmission that is independent of impurity arrangement direction.

Contribution

It provides a detailed proof of a symmetry in electron transmission through correlated impurity arrays in a lattice, extending understanding beyond the continuum approximation.

Findings

Particles transmit identically regardless of impurity direction

Symmetry holds in the continuum limit and is proven for the lattice

Time evolution analysis shows regions where symmetry is broken

Abstract

Correlated, or extended, impurities play an important role in the transport properties of dirty metals. Here, we examine, in the framework of a tight-binding lattice, the transmission of a single electron through an array of correlated impurities. In particular we show that particles transmit through an impurity array in identical fashion, regardless of the direction of transversal. The demonstration of this fact is straightforward in the continuum limit, but requires a detailed proof for the discrete lattice. We also briefly demonstrate and discuss the time evolution of these scattering states, to delineate regions (in time and space) where the aforementioned symmetry is violated.