Suppression of one-dimensional weak localization by band asymmetry

We investigate disorder-induced localization in metals that break time-reversal and inversion symmetries through their energy dispersion, ${\epsilon }_k\mathrm{\ne }{\epsilon }_{-k}$, 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 $\xi \propto 1\mathrm{/}{\eta }^2$ for asymmetric bands than conventional symmetric ones.