# Suppression of one-dimensional weak localization by band asymmetry

## TL;DR

This paper demonstrates that band asymmetry in metals suppresses weak localization effects, leading to increased delocalization, with analytical and numerical evidence showing a dependence on disorder strength and velocity mismatch.

## Contribution

It reveals how energy dispersion asymmetry suppresses weak localization without Berry phases, supported by analytical calculations and numerical simulations.

## Key findings

- Weak localization is suppressed by band asymmetry.
- Participation ratio increases with band asymmetry, indicating delocalization.
- Localization length scales as 1/η² for weak disorder in asymmetric bands.

## Abstract

We investigate disorder-induced localization in metals that break time-reversal and inversion symmetries through their energy dispersion, $\epsilon_{k}\neq\epsilon_{-k}$, but lack Berry phases. In the perturbative regime of disorder, we show that weak localization is suppressed due to a mismatch of the Fermi velocities of left and right movers. To substantiate this analytical result, we perform quench numerics on chains shorter than the Anderson localization length -- the latter computed and verified to be finite using the recursive Green's function method -- and find a sharp rise in the saturation value of the participation ratio due to band asymmetry, indicating a tendency to delocalize. Interestingly, for weak disorder strength $\eta$, we see a better fit to the scaling behavior $\xi\propto1/\eta^{2}$ for asymmetric bands than conventional symmetric ones.