Floquet Hofstadter Butterfly on the Kagome and Triangular Lattices

Recently, the interactions of materials with light have attracted considerable interest from the materials science community. “Hofstadter’s butterfly” refers to a fractal energy spectrum which occurs when a perpendicular magnetic field of extreme magnitude distributes the electronic energy levels of a lattice in a pattern resembling a butterfly. Lattices with a Hofstadter spectrum exhibit quantum Hall conductance, and under the influence of periodic driving, produce pairs of counter-propagating chiral edge modes which are robust against static disorder. We use Floquet theory to theoretically study the influence of a periodic driving potential provided by monochromatic circularly and linearly polarized light on the Hofstadter butterfly energy spectrum and Chern numbers of Kagome and triangular lattices. We find that as the lattices are exposed to driving, dramatic changes in the energy spectrum occur: reflection symmetry is broken, band width is altered, band inversion is observed, and polarization directional dependence can be identified. Further, we identify polarization-directional dependence of the Chern numbers. This work is currently under review at Phys Rev B, and can be found on Arxiv: arXiv:1808.02057