Anomalous caustics and Veselago focusing in 8-Pmmn borophene p-n junctions with arbitrary junction directions

TL;DR

This paper investigates how tilted massless Dirac fermions in 8-Pmmn borophene p-n junctions exhibit unique negative refraction phenomena, including anomalous caustics and Veselago focusing, depending on junction orientation and doping.

Contribution

It introduces a novel Green's function method for arbitrary junction directions and reveals direction-dependent interference patterns and caustics in tilted MDFs.

Findings

Veselago focusing occurs when junction is perpendicular to tilt.

Anomalous caustics emerge with certain junction orientations.

Green's function technique effectively models transport in tilted MDF systems.

Abstract

Negative refraction usually demands complex structure engineering while it is very natural for massless Dirac fermions (MDFs) across the \textit{p-n} junction, this leads to Dirac electron optics. The emergent Dirac materials may exhibit hitherto unidentified phenomenon due to their nontrivial band structures in contrast to the isotropic MDFs in graphene. Here, as a specific example, we explore the negative refraction induced caustics and Veselago focusing of tilted MDFs across 8-\textit{Pmmn} borophene \textit{p-n} junctions. To this aim, we develop a technique to effectively construct the electronic Green's function in \textit{p-n} junctions with arbitrary junction directions. Based on analytical discussions and numerical calculations, we demonstrate the strong dependence of interference pattern on the junction direction. As the junction direction perpendicular to the tilt direction, Veselago focusing or normal caustics (similar to that in graphene) appears resting on the doping configuration of the \textit{p-n} junctions, otherwise anomalous caustics (different from that in graphene) occurs which is manipulated by the junction direction and the doping configuration. Finally, the developed Green's function technique is generally promising to uncover the unique transport of emergent MDFs, and the discovered anomalous caustics makes tilted MDFs potential applications in Dirac electron optics.