`Holographic' treatment of surface disorder on a topological insulator

Abstract

The effect of surface disorder on electronic systems is particularly interesting for topological phases with surface and edge states. Using exact diagonalization, it has been demonstrated that the surface states of a 3D topological insulator survive strong surface disorder, and simply get pushed to a clean part of the bulk. Here we explore a new method which analytically eliminates the clean bulk, and reduces a $D$-dimensional problem to a Hamiltonian-diagonalization problem within the $(D-1)$-dimensional disordered surface. This dramatic reduction in complexity allows the analysis of significantly bigger systems than is possible with exact diagonalization. We use our method to analyze a 2D topological spin-Hall insulator with non-magnetic and magnetic edge impurities, and we calculate the probability density (or local density of states) of the zero-energy eigenstates as a function of edge-parallel momentum and layer index. Our analysis reveals that the system size needed to reach behavior in the thermodynamic limit increases with disorder. We also compute the edge conductance as a function of disorder strength, and chart a lower bound for the length scale marking the crossover to the thermodynamic limit.

12 pages, 9 figures

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Cited by in corpus (6)

• Boundary Green functions of topological insulators and superconductors
• Surface Green's functions and boundary modes using impurities: Weyl semimetals and topological insulators
• Sputtering induced re-emergence of the topological surface state in Bi${}_2$Se${}_3$
• Spatially varying electronic dephasing in three dimensional topological insulators
• Effect of surface disorder on the chiral surface states of a three-dimensional quantum Hall system
• Exact lattice-model calculation of boundary modes for Weyl semimetals and graphene