Replica higher-order topology of Hofstadter butterflies in twisted bilayer graphene

The Hofstadter energy spectrum of twisted bilayer graphene(TBG)is found to have recursive higher-order topological properties.We demonstrate that higher-order topological insulator(HOTI)phases,characterized by localized corner states,occur as replicas of the original HOTIs to fulfill the self-similarity of the Hofstadter spectrum.We show the existence of exact flux translational symmetry in TBG at all commensurate angles.Based on this result,we identify that the original HOTI phase at zero flux is re-entrant at a half-flux periodicity,where the effective twofold rotation is preserved.In addition,numerous replicas of the original HOTIs are found for fluxes without protecting symmetries.Like the original HOTIs,replica HOTIs feature both localized corner states and edge-localized real-space topological markers.The replica HOTIs originate from the different interaction scales,namely,intralayer and interlayer couplings,in TBG.The topological aspect of Hofstadter butterflies revealed in our results highlights symmetry-protected topology in quantum fractals.

Bloch theorem dictated wave chaos in microcavity crystals

Universality class of wave chaos emerges in many areas of science,such as molecular dynamics,optics,and network theory.In this work,we generalize the wave chaos theory to cavity lattice systems by discovering the intrinsic coupling of the crystal momentum to the internal cavity dynamics.The cavity-momentum locking substitutes the role of the deformed boundary shape in the ordinary single microcavity problem,providing a new platform for the in situ study of microcavity light dynamics.The transmutation of wave chaos in periodic lattices leads to a phase space reconfiguration that induces a dynamical localization transition.The degenerate scar-mode spinors hybridize and non-trivially localize around regular islands in phase space.In addition,we find that the momentum coupling becomes maximal at the Brillouin zone boundary,so the intercavity chaotic modes coupling and wave confinement are significantly altered.Our work pioneers the study of intertwining wave chaos in periodic systems and provide useful applications in light dynamics control.

Strong interlayer coupling and stable topological flat bands in twisted bilayer photonic Moiré superlattices

The moiré superlattice of misaligned atomic bilayers paves the way for designing a new class of materials with wide tunability.In this work,we propose a photonic analog of the moiré superlattice based on dielectric resonator quasi-atoms.In sharp contrast to van der Waals materials with weak interlayer coupling,we realize the strong coupling regime in a moiré superlattice,characterized by cascades of robust flat bands at large twist-angles.Surprisingly,we find that these flat bands are characterized by a non-trivial band topology,the origin of which is the moiré pattern of the resonator arrangement.The physical manifestation of the flat band topology is a robust one-dimensional conducting channel on edge,protected by the reflection symmetry of the moiré superlattice.By explicitly breaking the underlying reflection symmetry on the boundary terminations,we show that the first-order topological edge modes naturally deform into higher-order topological corner modes.Our work pioneers the physics of topological phases in the designable platform of photonic moiré superlattices beyond the weakly coupled regime.