We present an analysis of a square-lattice Harper-Hofstadter model with a periodically varying magnetic flux with time. By switching the dimensionless flux per plaquette between a set of values $\{p_j/q_j\}$ the Floquet quasienergy spectrum is folded into $Q=\mathrm{lcm}\left\{q_j\right\}$ bands. We determine closed-form analytical solutions for the quasienergy spectrum and Chern numbers for the $-1/2\to 1/2$ flux-switching case, as well as the Rudner-Lindner-Berg-Levin (RLBL) winding invariants $W$ numerically, and construct the corresponding topological phase diagram for arbitrary driving period. We find that generic flux-switching drives feature interlaced Hofstadter butterfly quasienergy spectra which may host Floquet topological phases with no static counterpart, and the gaps in the spectrum may be labeled according to a Diophantine equation which relates the quasienergy gap index to the fluxes attained in the drive and their associated per-step windings.

Close

PrevNext

View figure in article

• Density of states
• Edge states
• Electronic structure
• Floquet systems
• Topological materials