Flat-lens focusing of electrons on the surface of a topological insulator

We propose the implementation of an electronic Veselago lens on the conducting surface of a three-dimensional topological insulator (such as Bi₂Te₃). The negative refraction needed for such a flat lens results from the sign change in the curvature of the Fermi surface, changing from a circular to a snowflakelike shape across a sufficiently large electrostatic potential step. No interband transition (as in graphene) is needed. For this reason, and because the topological insulator provides protection against backscattering, the potential step is able to focus a broad range of incident angles. We calculate the quantum interference pattern produced by a point source, generalizing the analogous optical calculation to include the effect of a noncircular Fermi surface (having a nonzero conic constant).