The focusing effect of electron flow and negative refraction in three dimensional topological insulators

TL;DR

This paper demonstrates that electron flow can be focused by a p-n junction in three-dimensional topological insulators, acting as a Veselago lens, with effects robust against disorder and magnetic fields, indicating a general negative refraction phenomenon.

Contribution

It reveals the focusing effect of electron flow in 3D topological insulators as a Veselago lens, extending negative refraction concepts beyond 2D systems and analyzing robustness under disorder and magnetic fields.

Findings

Electron flow focuses at symmetric positions in the p region.

Focusing occurs both within and beyond the bulk energy gap.

Focusing effect is robust against moderate disorder and magnetic fields.

Abstract

We studied the focusing effect of electron flow induced by a single p-n junction (PNJ) in three-dimensional topological insulator. It is found that the electrons flowing from the n region can be focused at the symmetric position in the p region, acting as a perfect Veselago lens, regardless whether the incident energy is within or beyond the bulk energy gap. In the former case, the focusing effect occurs only in the surfaces. While in the latter case, the focusing effect occurs beyond the surfaces. These results show that the focusing effect of electron flow is a general phenomenon. It means the negative refraction may arise in all materials that are described by the massive or massless Dirac equation of 2D or beyond 2D system. Furthermore, we also find the focusing effect is robust in resisting the moderate random disorders. Finally, in the presence of a weak perpendicular magnetic field, the focusing effect remains well except that the position of the focal point is deflected by the transverse Lorentz force. Due to the finite size effect, the position of focal point oscillates periodically with a period of Delta B.