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

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 × 4 system of dynamical equations as two time-reversal related two-level problems, the quasienergy spectrum and the related dynamics are investigated via various techniques and approximations. In the static case, the system is 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 that are 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 (suppressions) are correlated to spin-up (down) phases.

Universal high-frequency behavior of periodically driven systems: from dynamical stabilization to Floquet engineering

“…13 for a schematic representation) have already been made for bosons using constant pulse sequences [134][135][136][137]. For fermions, the periodically driven spin-orbit coupling has been studied in graphene [138].…”

Graphene with time-dependent spin-orbit coupling: truncated Magnus expansion approach

“…This result simplifies (but is equivalent to) the approach given previously in Ref. [5] in that it avoids explicit reference to an initial time.…”

“…One alternative route which avoids the infinite dimensional eigenvalue formulation was put forward by Magnus [3,4] who proposed an exponential solution for the evolution operator given in terms of nested commutators of the time-dependent Hamiltonian. In a previous work [5] some of us have used the Magnus expansion (ME) in order to analyze the role of an ac-driven Rashba spin-orbit coupling (RSOC) on the spin dynamics of charge carriers in single layer graphene. However, as it was pointed out recently by Zhou and Wu [6], the reported results where beyond the convergence region of the ME solution.…”

Generalized Hamiltonian for a graphene subjected to arbitrary in-plane strains

“…94,95 Recently, Rashba SOI is extensively used in the tunable spin transport. [96][97][98][99][100][101][102][103][104] Another way is the proximity effect between a ferromagnetic insulator and graphene, 105 which induces the ferromagnetic graphene and has been demonstrated in experiments. 106,107 For the graphene valleytronics, the valley valve, filter and polarization also need to be realized.…”