Relativistic tunneling and accelerated transmission

TL;DR

This paper investigates relativistic quantum tunneling through electrostatic barriers, demonstrating conditions for accelerated and superluminal transmission, and clarifies misconceptions from non-relativistic models, with implications for graphene-based experiments.

Contribution

It provides exact solutions for relativistic tunneling, quantifies conditions for accelerated and superluminal transmission, and addresses previous non-relativistic interpretation issues.

Findings

Conditions for accelerated tunneling are precisely characterized.

Superluminal tunneling probabilities are demonstrated and explained.

Insights applicable to graphene electrostatic barrier experiments.

Abstract

We obtain the solutions for the tunneling zone of a one-dimensional electrostatic potential in the relativistic (Dirac to Klein-Gordon) wave equation regime when the incoming wave packet exhibits the possibility of being almost totally transmitted through the potential barrier. The conditions for the occurrence of accelerated and, eventually, superluminal tunneling transmission probabilities are all quantified and the problematic superluminal interpretation originated from the study based on non-relativistic dynamics of tunneling is overcome. The treatment of the problem suggests revealing insights into condensed-matter experiments using electrostatic barriers in single- and bi-layer graphene, for which the accelerated tunneling effect deserves a more careful investigation.