Multifractality at non-Anderson disorder-driven transitions in Weyl semimetals and other systems

TL;DR

This paper investigates the multifractal nature of wavefunctions at non-Anderson disorder-driven transitions in systems with power-law dispersion, revealing persistent fractal behavior across various models and dimensions.

Contribution

It demonstrates that multifractality exists at these transitions even when localization is prevented by symmetry or topology, and provides explicit spectra calculations using renormalisation-group methods.

Findings

Wavefunctions exhibit multifractality at disorder-driven transitions.

Multifractality persists despite symmetry or topological constraints.

Explicit spectra are calculated for semiconductors and Weyl semimetals.

Abstract

Systems with the power-law quasiparticle dispersion $\epsilon_{\bf k}\propto k^\alpha$ exhibit non-Anderson disorder-driven transitions in dimensions $d>2\alpha$, as exemplified by Weyl semimetals, 1D and 2D arrays of ultracold ions with long-range interactions, quantum kicked rotors and semiconductor models in high dimensions. We study the wavefunction structure in such systems and demonstrate that at these transitions they exhibit fractal behaviour with an infinite set of multifractal exponents. The multifractality persists even when the wavefunction localisation is forbidden by symmetry or topology and occurs as a result of elastic scattering between all momentum states in the band on length scales shorter than the mean free path. We calculate explicitly the multifractal spectra in semiconductors and Weyl semimetals using one-loop and two-loop renormalisation-group approaches slightly above the marginal dimension $d=2\alpha$.