Abstract
The Weyl semimetals are topologically protected from a gap opening against weak disorder in three dimensions. However, a strong disorder drives this relativistic semimetal through a quantum transition towards a diffusive metallic phase characterized by a finite density of states at the band crossing. This transition is usually described by a perturbative renormalization group in of a Gross-Neveu model in the limit . Unfortunately, this model is not multiplicatively renormalizable in dimensions: An infinite number of relevant operators are required to describe the critical behavior. Hence its use in a quantitative description of the transition beyond one loop is at least questionable. We propose an alternative route, building on the correspondence between the Gross-Neveu and Gross-Neveu-Yukawa models developed in the context of high-energy physics. It results in a model of Weyl fermions with a random non-Gaussian imaginary potential which allows one to study the critical properties of the transition within a expansion. We also discuss the characterization of the transition by the multifractal spectrum of wave functions.
- Received 18 May 2016
- Revised 12 September 2016
DOI:https://doi.org/10.1103/PhysRevB.94.220201
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