Genesis of the Floquet Hofstadter butterfly

TL;DR

This paper explores how circularly polarized light influences the Hofstadter butterfly spectrum in a graphene-like honeycomb lattice under magnetic fields, revealing tunable topological gaps and new spectral features across different frequency regimes.

Contribution

It introduces a Floquet-based theoretical analysis of the Hofstadter spectrum in driven graphene-like systems, highlighting the emergence of wing-like gaps and topological features.

Findings

Resonances create intricate topological gaps at low frequencies.

New wing-like gaps appear in the Landau-level regime with frequency tuning.

Gaps at zero energy open and close with increasing driving amplitude.

Abstract

We investigate theoretically the spectrum of a graphene-like sample (honeycomb lattice) subjected to a perpendicular magnetic field and irradiated by circularly polarized light. This system is studied using the Floquet formalism, and the resulting Hofstadter spectrum is analyzed for different regimes of the driving frequency. For lower frequencies, resonances of various copies of the spectrum lead to intricate formations of topological gaps. In the Landau-level regime, new wing-like gaps emerge upon reducing the driving frequency, thus revealing the possibility of dynamically tuning the formation of the Hofstadter butterfly. In this regime, an effective model may be analytically derived, which allows us to retrace the energy levels that exhibit avoided crossings and ultimately lead to gap structures with a wing-like shape. At high frequencies, we find that gaps open for various fluxes at $E=0$, and upon increasing the amplitude of the driving, gaps also close and reopen at other energies. The topological invariants of these gaps are calculated and the resulting spectrum is elucidated. We suggest opportunities for experimental realization and discuss similarities with Landau-level structures in non-driven systems.