Floquet M\"obius topological insulators

TL;DR

This paper introduces a new class of Floquet M"obius topological insulators with edge bands twisted around quasienergy $\

Contribution

It reveals Floquet M"obius topological phases characterized by generalized winding numbers, extending static M"obius insulators to nonequilibrium systems.

Findings

Interconnected M"obius edge bands around zero and $\\pi$ quasienergies.

Topological characterization by generalized winding numbers.

Numerical evidence from quasienergy and entanglement spectra.

Abstract

M\"obius topological insulators have dispersive edge bands with M\"obius twists in momentum space, which are protected by the combination of chiral and $Z_2$-projective translational symmetries. In this work, we reveal a unique type of M\"obius topological insulator, whose edge bands could twist around the quasienergy $\pi$ of a periodically driven system and are thus of Floquet origin. By applying time-periodic quenches to an experimentally realized M\"obius insulator model, we obtain interconnected M\"obius edge bands around zero and $\pi$ quasienergies, which can coexist with a gapped or gapless bulk. These M\"obius bands are topologically characterized by a pair of generalized winding numbers, which are integer-quantized due to an emergent chiral symmetry at a high-symmetry point in momentum space. Numerical investigations of the quasienergy and entanglement spectra provide consistent evidence for the presence of such M\"obius topological phases. A protocol based on the adiabatic switching of edge-band populations is further introduced to dynamically characterize the topology of Floquet M\"obius edge bands. Our findings thus extend the scope of M\"obius topological phases to nonequilibrium settings and unveil a unique class of M\"obius-twisted topological edge states without static counterparts.