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.

arXiv comment9+ pages

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• Systematic generation of the cascade of anomalous dynamical first and higher-order modes in Floquet topological insulators
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• Generation of higher-order topological insulators using periodic driving
• Chiral limits and effect of light on the Hofstadter butterfly in twisted bilayer graphene
• Polarization as a tuning parameter for Floquet engineering: magnetism in the honeycomb, square, and triangular Mott insulators
• Photoinduced Floquet topological magnons in a ferromagnetic checkerboard lattice
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• Tailoring Metal Insulator Transitions $\&$ Band Topology via Off-resonant Periodic Drive in an Interacting Triangular Lattice
• From linear to circular polarized light -- Floquet engineering in Kitaev-Heisenberg materials with Lissajous figures
• The Future of the Correlated Electron Problem
• Floquet states in (LaNiO${}_3$)${}_2$/(LaAlO${}_3$)${}_N$ heterostructures grown along the (111) direction
• Spin-dependent Andreev reflection in spin-orbit coupled systems by breaking time-reversal symmetry
• Low-frequency and Moiré Floquet engineering: a review
• Floquet engineering and non-equilibrium topological maps in twisted trilayer graphene