Multifractal nature of the surface local density of states in three-dimensional topological insulators with magnetic and nonmagnetic disorder

TL;DR

This paper analyzes the multifractal properties of local density of states fluctuations on the surfaces of three-dimensional topological insulators with magnetic and non-magnetic disorder, revealing different scaling behaviors and corrections.

Contribution

It provides the first detailed computation of multifractal spectra for LDOS in disordered topological insulator surfaces, highlighting differences between magnetic and non-magnetic impurities.

Findings

Magnetic impurities induce quadratic multifractality at first order.

Non-magnetic impurities show no multifractal scaling at first order.

Spectral enhancement occurs near the Dirac point due to renormalization.

Abstract

We compute the multifractal spectra associated to local density of states (LDOS) fluctuations due to weak quenched disorder, for a single Dirac fermion in two spatial dimensions. Our results are relevant to the surfaces of Z_2 topological insulators such as Bi_2Se_3 and Bi_2Te_3, where LDOS modulations can be directly probed via scanning tunneling microscopy. We find a qualitative difference in spectra obtained for magnetic versus non-magnetic disorder. Randomly polarized magnetic impurities induce quadratic multifractality at first order in the impurity density; by contrast, no operator exhibits multifractal scaling at this order for a non-magnetic impurity profile. For the time-reversal invariant case, we compute the first non-trivial multifractal correction, which appears at two loops (impurity density squared). We discuss spectral enhancement approaching the Dirac point due to renormalization, and we survey known results for the opposite limit of strong disorder.