# Unexpected effects in periodic driving of gapless topological systems

**Abstract**: Floquet engineering is the emerging field of using periodic drive to realize novel Hamiltonians that are difficult or impossible to realize in static systems. In this talk I will highlight two examples where such a drive yields unexpected effects. First, I will discuss Floquet engineering of Weyl semimetals, which has been proposed for ultracold atoms in optical lattices. Unlike their condensed matter counterparts, these systems naturally have large magnetic fields whose two-dimensional physics is described by the Hofstadter butterfly. I will show how one realizes it natural extension, the "Weyl butterfly," in a three-dimensional Weyl semimetal and discuss how the chiral anomaly generalizes beyond the weak-field limit. In particular, I will describe how the chiral anomaly inherits the fractal structure of the Weyl butterfly, exhibiting a fractal set of quantized anomalies that originate from the gaps of the butterfly. Second, I will switch gears to a condensed matter realization of Floquet engineering, namely periodic driving of surface states in topological insulators. While in the absence of driving surface states are well-defined gapped excitations, I will show that driving the surface of such system naturally leads to resonant surface-bulk coupling. Furthermore, this coupling leads to coherent bulk-surface oscillations in the Wigner distribution -- a non-equilbrium observable measurable via ARPES -- and may be responsible for the non-adiabatic signal seen in recent experiments.

**Series:**IQIM Postdoctoral and Graduate Student Seminar Series