1111.6639 (Matthew S. Foster)

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

Matthew S. Foster

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.

View original: http://arxiv.org/abs/1111.6639