Theory of the random potential and conductivity at the surface of a topological insulator

Abstract

We study the disorder potential induced by random Coulomb impurities at the surface of a topological insulator (TI). We use a simple model in which positive and negative impurities are distributed uniformly throughout the bulk of the TI, and we derive the magnitude of the disorder potential at the TI surface using a self-consistent theory based on the Thomas-Fermi approximation for screening by the Dirac mode. Simple formulas are presented for the mean squared potential both at the Dirac point and far from it, as well as for the characteristic size of electron/hole puddles at the Dirac point and the total concentration of electrons/holes that they contain. We also derive an expression for the autocorrelation function for the potential at the surface and show that it has an unusually slow decay, which can be used to verify the bulk origin of disorder. The implications of our model for the electron conductivity of the surface are also presented.

arXiv comment6 pages, 2 figures; section about conductivity added

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Cited by in corpus (23)

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• Coulomb disorder in three-dimensional Dirac systems
• Filling of magnetic-impurity-induced gap in topological insulators by potential scattering
• Majorana bound states in topological insulators without a vortex
• Gate-tunable flat bands in van der Waals patterned dielectric superlattices
• Effect of bulk charged impurities on the bulk and surface transport in three-dimensional topological insulators
• Current-induced breakdown of the quantum anomalous Hall effect
• Van der Waals heterostructures with spin-orbit coupling
• Conductivity of two-dimensional narrow gap semiconductors subjected to strong Coulomb disorder
• Length scale of puddle formation in compensation-doped semiconductors and topological insulators
• Hyers-Ulam stability of elliptic Möbius difference equation
• Disorder effects in topological insulator thin films
• Metallization and proximity superconductivity in topological insulator nanowires
• Disorder effects in topological insulator nanowires
• 2D-Dirac surface states and bulk gap probed via quantum capacitance in a 3D topological insulator
• Upper bound on the window of density occupied by microemulsion phases in two-dimensional electron systems
• Conductivity of two-dimensional small gap semiconductors and topological insulators in strong Coulomb disorder
• Effect of impurities on the Josephson current through helical metals: Exploiting a neutrino paradigm
• Ambipolar magneto-optical response of ultra-low carrier density topological insulators
• Characterizing the chemical potential disorder in the topological insulator (Bi${}_{1-x}$Sb${}_x$)${}_2$Te${}_3$ thin films
• Hydrodynamics of the electronic Fermi liquid: a pedagogical overview
• Observation of the surface hybridization gap in the electrical transport properties of the ultrathin topological insulator (Bi${}_{1-x}$Sb${}_x$)${}_2$Te${}_3$