# Multifractality at the Weyl semimetal-diffusive metal transition for generic disorder

## TL;DR

This paper investigates the multifractal properties of wave functions at the transition from a Weyl semimetal to a diffusive metal, analyzing how disorder correlation range influences critical behavior using renormalization group methods.

## Contribution

It introduces a detailed study of the multifractal spectrum at the transition, considering generic disorder including scalar and vector potentials, and derives a new scaling relation for the local density of states.

## Key findings

- Multifractal spectrum varies with disorder correlation range.
- Derived a new scaling relation for the typical local DOS.
- Applied findings to disordered semiconductors with power-law dispersion.

## Abstract

A Weyl semimetal is a three dimensional topological gapless phase. In the presence of strong enough disorder it undergoes a quantum transition towards a diffusive metal phase whose universality class depends on the range of disorder correlations. Similar to other quantum transitions driven by disorder, the critical wave functions at the semimetal-diffusive metal transition exhibit multifractality. Using renormalization group methods we study the corresponding multifractal spectrum as a function of the range of disorder correlations for generic disorder including random scalar and vector potentials. We also discuss the relation between the geometric fluctuations of critical wave functions and the broad distribution of the local density of states (DOS) at the transition. We derive a new scaling relation for the typical local DOS and argue that it holds for other disorder-driven transitions in which both the average and typical local DOS vanish on one side of the transition. As an illustration we apply it to the recently discussed unconventional quantum transition in disordered semiconductors with power-law dispersion relation near the band edge.