Weak localization and crossover from Lifshitz transition in two dimensions

Dirac point plays a crucial role in regulating electronic properties of topological semimetals. In two dimensions, the manipulation of Dirac points can spur a transition from Dirac semimetal through semi-Dirac phase to a gapped phase. Across such a so-called Lifshitz transition, we find that the quantum interference corrections to the conductivity delta sigma(xx) and delta sigma(yy) are always negative, giving rise to a weak localization behavior. The ratio delta sigma(xx)/delta sigma(yy) undergoes a transition from linear to parabolic dependence on the merging parameter across the Lifshitz transition, which leads to a crossover of the temperature dependence of the inverse inelastic scattering time 1/T epsilon from similar to T to similar to T ln(T-0/T). This fingerprint behavior can be readily tested experimentally through merging Dirac points in two-dimensional lattices. This work presents an alternative perspective to understand weak localization through Lifshitz transition.