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

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.

16 pages, 4 figures; v2 references updated, published version

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Cited by in corpus (22)

• Quantum frequency doubling in the topological insulator Bi2Se3
• Anderson localization and the quantum phase diagram of three dimensional disordered Dirac semimetals
• Statistics of eigenstates near the localization transition on random regular graphs
• Topological protection, disorder, and interactions: Survival at the surface of 3D topological superconductors
• Global Phase Diagram of a Dirty Weyl Liquid and Emergent Superuniversality
• On the disorder-driven quantum transition in three-dimensional relativistic metals
• Interaction-mediated surface state instability in disordered three-dimensional topological superconductors with spin SU(2) symmetry
• Effects of the Dirac cone tilt in two-dimensional Dirac semimetal
• The theory of avoided criticality in quantum motion in a random potential in high dimensions
• Multifractality at non-Anderson disorder-driven transitions in Weyl semimetals and other systems
• Condition for the emergence of a bulk Fermi arc in disordered Dirac-fermion systems
• Quantum phase transition and unusual critical behavior in multi-Weyl semimetals
• Superconductivity in two-dimensional disordered Dirac semimetals
• Multifractality at the Weyl semimetal-diffusive metal transition for generic disorder
• Gapless helical superconductivity on the surface of a three-dimensional topological insulator
• Effects of random potentials in three-dimensional quantum electrodynamics
• Emergent space-time supersymmetry at disorder quantum critical point
• Interplay between tilt, disorder, and Coulomb interaction in type-I Dirac fermions
• Nested Defects on the Boundary of Topological Superconductors
• Fate of superconductivity in disordered Dirac and semi-Dirac semimetals
• Global phase diagram of Coulomb-interacting anisotropic Weyl semimetals with disorder
• Quantum Fractality on the Surface of Topological Insulators