Longwen Zhou

The discovery of critical points that can host quantized nonlocal order parameters and degenerate edge modes relocates the study of symmetry-protected topological phases (SPTs) to gapless regions. In this Letter, we reveal gapless SPTs (gSPTs) in systems tuned out of equilibrium by periodic drivings and non-Hermitian couplings. Focusing on one-dimensional models with sublattice symmetry, we introduce winding numbers by applying the Cauchy's argument principle to generalized Brillouin zone, yielding unified topological characterizations and bulk-edge correspondence both in gapped phases and at gapless critical points. The theory is demonstrated in a broad class of Floquet bipartite lattices, unveiling unique topological criticality of non-Hermitian Floquet origin. Our findings identify gSPTs in driven open systems and uncover robust topological edge modes at phase transitions beyond equilibrium.

The discovery of critical points that can host quantized nonlocal order parameters and degenerate edge modes relocate the study of symmetry-protected topological phases (SPTs) to gapless regions. In this letter, we reveal gapless SPTs (gSPTs) in systems tuned out-of-equilibrium by periodic drivings and non-Hermitian couplings. Focusing on one-dimensional models with sublattice symmetry, we introduce winding numbers by applying the Cauchy's argument principle to generalized Brillouin zone (GBZ), yielding unified topological characterizations and bulk-edge correspondence in both gapped phases and at gapless critical points. The theory is demonstrated in a broad class of Floquet bipartite lattices, unveiling unique topological criticality of non-Hermitian Floquet origin. Our findings identify gSPTs in driven open systems and uncover robust topological edge modes at phase transitions beyond equilibrium.

Non-Abelian topological insulators are characterized by matrix-valued, non-commuting topological charges with regard to more than one energy gap. Their descriptions go beyond the conventional topological band theory, in which an additive integer like the winding or Chern number is endowed separately with each (degenerate group of) energy band(s). In this work, we reveal that Floquet (time-periodic) driving could not only enrich the topology and phase transitions of non-Abelian topological matter, but also induce bulk-edge correspondence unique to nonequilibrium setups. Using a one-dimensional (1D), three-band model as an illustrative example, we demonstrate that Floquet driving could reshuffle the phase diagram of the non-driven system, yielding both gapped and gapless Floquet band structures with non-Abelian topological charges. Moreover, by dynamically tuning the anomalous Floquet π-quasienergy gap, non-Abelian topological transitions inaccessible to static systems could arise, leading to much more complicated relations between non-Abelian topological charges and Floquet edge states. These discoveries put forth periodic driving as a powerful scheme of engineering non-Abelian topological phases (NATPs) and incubating unique non-Abelian band topology beyond equilibrium.