# Synopsis: Dirt and geometry insulate electrons

#### Topological Anderson Insulator

Jian Li, Rui-Lin Chu, J. K. Jain, and Shun-Qing Shen

Published April 1, 2009

Random disorder can render a two-dimensional system of noninteracting electrons into an insulating state known as the Anderson insulator [1]. Another well-known manifestation of two-dimensional physics—the integer quantum Hall effect—is the formation of dissipationless current-carrying edge states in the presence of a magnetic field.

Writing in Physical Review Letters, Jian Li, Rui-Lin Chu, and Shung-Qing Shen of The University of Hong Kong and Jainendra Jain of Pennsylvania State University in the US address how disorder affects edge states in topological insulators, a class of band insulators that exhibit strange conduction properties similar to what is seen in quantum Hall states, but in the absence of an external magnetic field. (See also the Viewpoint on topological insulators [2].)

It is known that the physics of topological insulators is immune to weak disorder. However, the authors also predict a surprising phase in $\text{HgTe/CdTe}$ quantum well topological insulators. They call this phase the topological Anderson insulator, where disorder introduces two key differences from previously studied topological insulators: The Fermi energy lies in a so-called mobility gap, as opposed to a “real” gap, and the edge states do not appear to depend on the specific band structure of the quantum wells. That said, these $\text{HgTe/CdTe}$ quantum wells possess an “inverted” band structure and offer the possibility to considerably tweak their transport and structure properties, which in turn promises further insights into how disorder and doping modify the phase diagram of topological insulators. – Sami Mitra

[1] E. Abrahams, Phys. Rev. Lett. 42, 673 (1979).

[2] S. C. Zhang, Physics 1, 6 (2008).