Hartman effect and spin precession in graphene

TL;DR

This paper demonstrates that at the Dirac point in clean graphene, the transmission time for electrons exhibits the Hartman effect, appearing shorter than expected, which is analogous to superluminal phenomena observed in optics.

Contribution

It reveals the Hartman effect in graphene's electron transmission time at the Dirac point, providing a novel quantum optical analogy in condensed matter physics.

Findings

Transmission time  L/v at the Dirac point

Observation of apparent superluminality in graphene

Interpretation of results as Hartman effect

Abstract

Spin precession has been used to measure the transmission time \tau over a distance L in a graphene sheet. Since conduction electrons in graphene have an energy-independent velocity v, one would expect \tau > L/v. Here we calculate that \tau < L/v at the Dirac point (= charge neutrality point) in a clean graphene sheet, and we interpret this result as a manifestation of the Hartman effect (apparent superluminality) known from optics.