Topological insulators in random potentials

Abstract

We investigate the effects of magnetic and nonmagnetic impurities on the two-dimensional surface states of three-dimensional topological insulators (TIs). Modeling weak and strong TIs using a generic four-band Hamiltonian, which allows for a breaking of inversion and time-reversal symmetries and takes into account random local potentials as well as the Zeeman and orbital effects of external magnetic fields, we compute the local density of states, the single-particle spectral function, and the conductance for a (contacted) slab geometry by numerically exact techniques based on kernel polynomial expansion and Green's function approaches. We show that bulk disorder refills the suface-state Dirac gap induced by a homogeneous magnetic field with states, whereas orbital (Peierls-phase) disorder perserves the gap feature. The former effect is more pronounced in weak TIs than in strong TIs. At moderate randomness, disorder-induced conducting channels appear in the surface layer, promoting diffusive metallicity. Random Zeeman fields rapidly destroy any conducting surface states. Imprinting quantum dots on a TI's surface, we demonstrate that carrier transport can be easily tuned by varying the gate voltage, even to the point where quasi-bound dot states may appear.

final version, 8 pages, 14 figures

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• Quantum Valley Hall effect without Berry curvature
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• Conduction of surface electrons in a topological insulator with spatially random magnetization
• Spin Berry curvature of the Haldane model
• Doping-controlled surface conduction in topological insulators with warping effects
• A domain-specific language and matrix-free stencil code for investigating electronic properties of Dirac and topological materials
• Time-reversal invariant resonant backscattering on a topological insulator surface driven by a time-periodic gate voltage