Floquet spin states in graphene under ac driven spin-orbit interaction

TL;DR

This paper investigates how periodic ac driving of Rashba spin-orbit coupling in graphene affects its electronic and spin properties, revealing dynamic gap closing, spin polarization oscillations, and altered quantum interference patterns.

Contribution

It introduces a comprehensive analysis of Floquet spin states in graphene under ac-driven spin-orbit interaction, highlighting the limitations of the RWA and demonstrating dynamic gap closure and spin polarization effects.

Findings

Dynamic closing of the energy gap at the Dirac point.

Oscillating out-of-plane spin polarization in driven states.

Distorted interference patterns in autocorrelation functions due to ac driving.

Abstract

We study the role of periodically driven time-dependent Rashba spin-orbit coupling (RSOC) on a monolayer graphene sample. After recasting the originally $4\times 4$ system of dynamical equations as two time-reversal related two-level problems, the quasi-energy spectrum and the related dynamics are investigated via various techniques and approximations. In the static case the system is a gapped at the Dirac point. The rotating wave approximation (RWA) applied to the driven system unphysically preserves this feature, while the Magnus-Floquet approach as well as a numerically exact evaluation of the Floquet equation show that this gap is dynamically closed. In addition, a sizable oscillating pattern of the out-of-plane spin polarization is found in the driven case for states which completely unpolarized in the static limit. Evaluation of the autocorrelation function shows that the original uniform interference pattern corresponding to time-independent RSOC gets distorted. The resulting structure can be qualitatively explained as a consequence of the transitions induced by the ac driving among the static eigenstates, i.e., these transitions modulate the relative phases that add up to give the quantum revivals of the autocorrelation function. Contrary to the static case, in the driven scenario, quantum revivals (suppresions) are correlated to spin up (down) phases.