Two-dimensional group delay in graphene probed by spin precession measurements

TL;DR

This paper demonstrates that the true 2D group delay in graphene includes an intrinsic component from the Goos-Hänchen shift, and proposes an experimental method to measure it via spin precession, revealing new insights into electron dynamics.

Contribution

It introduces a relation between 2D group delay and dwell time in graphene, highlighting the intrinsic GH shift contribution and proposing an experimental measurement approach.

Findings

The 2D group delay can be observed through conductance differences in spin precession experiments.

The intrinsic GH shift significantly affects the group delay in 2D ballistic systems.

Analytical solutions at the Dirac point elucidate the 2D Hartman effect.

Abstract

We take graphene as an example to demonstrate that the present widely adopted expression is only the scattering component of a true 2D group delay in the condensed matter context, in which the spatial Goos-H\"{a}nchen (GH) shift along an interface contributes an intrinsic component. We relate the dwell time to spin precession and derive a relation between the 2D group delay and dwell time, whereby we for the first time reveal that, the group delay for 2D ballistic electronic systems can be directly observed by measuring a conductance difference in a weak-field spin precession experiment. This physical observable not only implies the group delay being a relevant quantity even in the condensed matter context, but also provides an experimental evidence for the intrinsic effect of the GH shift. Finally, we revisit the 2D Hartman effect, a central issue of the group delay, by analytically solving it via the vested relation and calculating the proposed observable at the Dirac point.