Quantum critical exponents for a disordered three-dimensional Weyl node

Abstract

Three-dimensional Dirac and Weyl semimetals exhibit a disorder-induced quantum phase transition between a semimetallic phase at weak disorder and a diffusive-metallic phase at strong disorder. Despite considerable effort, both numerically and analytically, the critical exponents ν and z of this phase transition are not known precisely. Here we report a numerical calculation of the critical exponent ν=1.47±0.03 using a minimal single-Weyl node model and a finite-size scaling analysis of conductance. Our high-precision numerical value for ν is incompatible with previous numerical studies on tight-binding models and with one- and two-loop calculations in an ε-expansion scheme. We further obtain z=1.49±0.02 from the scaling of the conductivity with chemical potential.