Unconventional localization transition in high dimensions

Abstract

We study noninteracting systems with a power-law quasiparticle dispersion ${\ensuremath{\xi}}_{\mathbf{k}}\ensuremath{\propto}{k}^{\ensuremath{\alpha}}$ and a random short-range-correlated potential. We show that, unlike the case of lower dimensions, for $d>2\ensuremath{\alpha}$, there exists a critical disorder strength (set by the bandwidth), at which the system exhibits a disorder-driven quantum phase transition at the bottom of the band that lies in a universality class distinct from the Anderson transition. In contrast to the conventional wisdom, it manifests itself in, e.g., the disorder-averaged density of states. For systems in symmetry classes that permit localization, the striking signature of this transition is a nonanalytic behavior of the mobility edge, which is pinned to the bottom of the band for subcritical disorder and grows for disorder exceeding a critical strength. Focusing on the density of states, we calculate the critical behavior (exponents and scaling functions) at this novel transition, using a renormalization group, controlled by an $\ensuremath{\varepsilon}=d\ensuremath{-}2\ensuremath{\alpha}$ expansion. We also apply our analysis to Dirac materials, e.g., Weyl semimetals, where this transition takes place in physically interesting three dimensions.