Topological insulators in random potentials

TL;DR

This paper studies how magnetic and nonmagnetic impurities affect the surface states of topological insulators, revealing disorder-induced states, the impact of magnetic fields, and the tunability of surface conductance.

Contribution

It provides a comprehensive numerical analysis of impurity effects on topological insulator surface states, including disorder, magnetic fields, and quantum dot engineering.

Findings

Bulk disorder refills the Dirac gap with states in magnetic fields.

Orbital disorder preserves the surface gap.

Disorder induces metallic channels and can be tuned by gate voltage.

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.