Hartman effect and spin precession in graphene

Abstract

Spin precession has been used to measure the transmission time τover a distance L in a graphene sheet. Since conduction electrons in graphene have an energy-independent velocity v, one would expect τ> L/v. Here we calculate that τ< 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.

6 pages, 4 figures; v2: added a section on the case of perpendicularly aligned magnetizations; v3: added a figure