Veselago focusing of anisotropic massless Dirac fermions

TL;DR

This paper demonstrates precise Veselago focusing of anisotropic massless Dirac fermions in p-n junctions, offering tunable focusing positions for potential electron optics applications, expanding beyond isotropic MDF limitations.

Contribution

It introduces an analytical method to achieve Veselago focusing with anisotropic MDFs, enabling tunability and practical device design.

Findings

Exact analytical expression for propagator of anisotropic MDFs

Precise Veselago focusing without mirror symmetry constraints

Tunable focusing position for device applications

Abstract

Massless Dirac fermions (MDFs) emerge as quasiparticles in various novel materials such as graphene and topological insulators, and they exhibit several intriguing properties, of which Veselago focusing is an outstanding example with a lot of possible applications. However, up to now Veselago focusing merely occurred in p-n junction devices based on the isotropic MDF, which lacks the tunability needed for realistic applications. Here, motivated by the emergence of novel Dirac materials, we investigate the propagation behaviors of anisotropic MDFs in such a p-n junction structure. By projecting the Hamiltonian of the anisotropic MDF to that of the isotropic MDF and deriving an exact analytical expression for the propagator, precise Veselago focusing is demonstrated without the need for mirror symmetry of the electron source and its focusing image. We show a tunable focusing position that can be used in a device to probe masked atom-scale defects. This study provides an innovative concept to realize Veselago focusing relevant for potential applications, and it paves the way for the design of novel electron optics devices by exploiting the anisotropic MDF.