A study of transit times in Dirac tunneling

TL;DR

This paper investigates relativistic electron tunneling using the Dirac equation, revealing superluminal transmission phenomena even in thin barriers, challenging traditional notions of tunneling velocities.

Contribution

It provides a new numerical analysis demonstrating superluminal tunneling in relativistic electrons for thin barriers, expanding understanding beyond previous opaque barrier results.

Findings

Superluminal transmission observed in thin barriers.

Transit velocity proportional to barrier width in opaque limit.

Relativistic effects lead to velocities exceeding c.

Abstract

Based on the Dirac equation, the behavior of relativistic electrons which tunnel a potential barrier of height V0 for incoming energies between V0 and V0+m is studied by using the wave packet formalism. The choice of this incoming energy zone guarantees that only electrons participate to the tunneling process. In the opaque limit, as shown in a previous analysis, the transit velocity is proportional to the barrier width and for relativistic potential tends to a constant value greater than $c$. In this paper, a new numerical study shows a very surprising result: superluminal transmissions are also evident for thin barriers.