Brillouin-Wigner Theory for Floquet Topological Phase Transitions in Spin-orbit Coupled Materials

Abstract

We develop the high frequency expansion based on the Brillouin-Wigner (B-W) perturbation theory for driven systems with spin-orbit coupling which is applicable to the cases of silicene, germanene and stanene. We compute the effective Hamiltonian in the zero photon subspace not only to order $O({\omega }^{-1})$, but by keeping all the important terms to order $O({\omega }^{-2})$, and obtain the photo-assisted correction terms to both the hopping and the spin-orbit terms, as well as new longer ranged hopping terms. We then use the effective static Hamiltonian to compute the phase diagram in the high frequency limit and compare it with the results of direct numerical computation of the Chern numbers of the Floquet bands, and show that at sufficiently large frequencies, the B-W theory high frequency expansion works well even in the presence of spin-orbit coupling terms.

9+ pages

References in corpus (11)

• Photovoltaic Hall effect in graphene
• Topological characterization of periodically-driven quantum systems
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• Effective Theory of Floquet Topological Transitions
• Dissipative Floquet Topological Systems
• Quantized Adiabatic Transport in Momentum Space
• Occupation of topological Floquet bands in open systems
• Floquet resonant states and validity of the Floquet-Magnus expansion in the periodically driven Friedrichs models

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• Chiral limits and effect of light on the Hofstadter butterfly in twisted bilayer graphene
• Photoinduced Floquet topological magnons in a ferromagnetic checkerboard lattice
• Time-dependent strain-tuning topological magnon phase transition
• Light driven magnetic transitions in transition metal dichalcogenide heterobilayers
• From linear to circular polarized light -- Floquet engineering in Kitaev-Heisenberg materials with Lissajous figures
• Low-frequency and Moiré Floquet engineering: a review
• Floquet engineering and non-equilibrium topological maps in twisted trilayer graphene