Hartman effect and spin precession in graphene

Abstract

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