  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.
