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Topology in photonics comes in two distinct flavors: global and local. Global topology considers invariants that are obtained by integrating over the energy band, whereas local topology considers defects, typically vortices, in the…

Coexistence of nontrivial topology and flat electronic bands in low-energy lattices provides a fertile platform for correlated quantum states. The square-octagon lattice hosts Dirac nodes and flat bands at half-filling, yet the influence of…

Topological semimetals with several types of three-dimensional (3D) fermion of electrons, such as Dirac fermions, Weyl fermions, Dirac nodal lines and triply degenerate nodal points have been theoretically predicted and then experimentally…

The destructive interference of wavefunctions in a kagome lattice can give rise to topological flat bands (TFBs) with a highly degenerate state of electrons. Recently, TFBs have been observed in several kagome metals, including…

By combining exotic band dispersion with nontrivial band topology, an interesting type of band structure, namely the flat chern band (FCB), has recently been proposed to spawn high-temperature fractional quantum hall states. Despite the…

Tilted lattice potentials with periodic driving play a crucial role in the study of artificial gauge fields and topological phases with ultracold quantum gases. However, driving-induced heating and the growth of phonon modes restrict their…

We report the appearance of multiple numbers of completely flat band states in an extended Lieb lattice model in two dimensions with five atomic sites per unit cell. We also show that this edge-centered square lattice can host intriguing…

We develop a unified view of topological phase transitions (TPTs) in solids by revising the classical band theory with the inclusion of topology. Re-evaluating the band evolution from an "atomic crystal" [a normal insulator (NI)] to a solid…

Recent theoretical works have demonstrated various robust Abelian and non-Abelian fractional topological phases in lattice models with topological flat bands carrying Chern number C=1. Here we study hard-core bosons and interacting fermions…

While condensed matter systems host both Fermionic and Bosonic quasi-particles, reliably predicting and empirically verifying topological states is only mature for Fermionic electronic structures, leaving topological Bosonic excitations…

Topological materials hosting multifold fermions and bosons have emerged as a rich platform for exploring unconventional quasiparticles and transport phenomena. In this work, we investigate the chiral crystal SiTc using first-principles…

We study bosonic atoms with two internal states in artificial gauge potentials whose strengths are different for the two components. A series of topological phases for such systems is proposed using the composite fermion theory and the…

Much of our understanding of vibrational excitations and elasticity is based upon analysis of frames consisting of sites connected by bonds occupied by central-force springs, the stability of which depends on the average number of neighbors…

Isolated flat bands with significantly quenched kinetic energy of electrons could give rise to exotic strongly correlated states from electron-electron interactions. More intriguingly, the interplay between topology and flat bands can…

We investigate superfluidity of bosons in gapped topological bands and discover a new phase that has no counterparts in the previous literature. This phase is characterized by a highly unconventional modulation of the order parameter,…

Magnetic topological semimetals, a novel state of quantum matter with nontrivial band topology, have emerged as a new frontier in physics and materials science. An external stimulus like temperature or magnetic field could be expected to…

The rapid advances in the study of fractional Chern insulators (FCIs) raise a fundamental question: while initially discovered in flat Chern bands motivated by their topological equivalence to Landau levels, is single- particle band…

An alternative method to the topological instanton solution for deriving an expression for the topological charge is presented. This alternative method involves the use of relativistic quantum field theory and covariant electrodynamics. In…

We show that a large class of two-dimensional spinless fermion models exhibit topological superconducting phases characterized by a non-zero Chern number. More specifically, we consider a generic one-band Hamiltonian of spinless fermions…

By means of group theory, topological quantum chemistry, first-principles and Monte Carlo calculations, we analyze the topology of the 2D buckled honeycomb lattice phonon spectra. Taking the pure crystal structure as an input, we show that…