Related papers: Topology invisible to eigenvalues in obstructed at…
Topological phases of matter are generally characterized by topological properties of energy bands of a system. Their transitions under preserved symmetries occur through closing a gap of energy bands, leading to topologically protected…
The BR, formulated by Zak in the 80s, is widely used in studies of topological phase of material. EBR are considered the building block of TQC. However, there were debate on whether they admit split bands, or if they contain band invariant…
We investigate the bulk-boundary correspondence for massless Dirac fermion in $\alpha$-${T}_3$ lattice where the Berry phase can be continuously tuned from $\pi $ (graphene) to $0$ ($T_3$ or dice lattice) without modifying the energy…
Recently, higher-order topological insulators have been attracting extensive interest. Unlike the conventional topological insulators that demand bulk gap closings at transition points, the higher-order band topology can be changed without…
Symmetry and its representation play a crucial role in topological phases, including both Hermitian and non-Hermitian paradigms. In the presence of synthetic gauge field, spatial symmetries should be projectively represented, which can…
The phase of quantum magneto-oscillations is often associated with the Berry phase and is widely used to argue in favor of topological nontriviality of the system (Berry phase $2\pi n+\pi$). Nevertheless, the experimentally determined value…
We classify insulators by generalized symmetries that combine space-time transformations with quasimomentum translations. Our group-cohomological classification generalizes the nonsymmorphic space groups, which extend point groups by…
A general free bosonic system with a pairing term is described by a bosonic Bogoliubov-de Gennes (BdG) Hamiltonian. The representation is given by a pseudo-Hermitian matrix, which is crucially different from the Hermitian representation of…
We demonstrate the existence of topologically nontrivial phase in a one-dimensional fermionic lattice system subjected to synthetic gauge fields, which is beyond the standard Altland-Zirnbauer classification of topological insulators. The…
Topology in quantum matter is typically associated with gapped phases. For example, in symmetry protected topological (SPT) phases, the bulk energy gap localizes edge modes near the boundary. In this work we identify a new mechanism that…
In investigating the topological electronic structures of monolayer $\alpha$-phase group V elements, we uncover a new topological phase, which is invisible in the symmetry-based topological quantum chemistry (TQC) as well as symmetry…
Bi$_{2}$Se$_{3}$ is a well known 3D-topological insulators(TI) with a non-trivial Berry phase of $ \left(2n+1\right)\pi $ attributed to the topology of the band structure. The Berry phase shows non-topological deviations from $…
We introduce a class of singular connections as an alternative to the Berry connection for any family of quantum states defined over a parameter space. We find a natural application of the singular connection in the context of transition…
Topological phases of matter lie at the heart of physics, connecting elegant mathematical principles to real materials that are believed to shape future electronic and quantum computing technologies. To date, studies in this discipline have…
Topological photonics is developed based on the analogy of Schr\"{o}dinger equation which is mathematically reduced to a standard eigenvalue equation. Notably, several photonic systems are beyond the standard topological band theory as they…
We examine excitons formed in the bulk of a topological insulator as the system is tuned via a parameter between topological and trivial insulating phases, arguing that nontrivial topology has fingerprints in the spectrum of these excitons.…
We consider chiral, generally nonlinear density waves in one dimension, modelling the bosonized edge modes of a two-dimensional fermionic topological insulator. Using the coincidence between bosonization and Lie-Poisson dynamics on an…
We study the topological characterization of the energy gaps in general two-dimensional quasiperiodic systems consisting of multiple periodicities, represented by twisted two-dimensional materials. We show that every single gap is uniquely…
We study infrared divergences in quantum electrodynamics using geometric phases and the adiabatic approximation in quantum field theory. In this framework, the asymptotic \textit{in} and \textit{out} states are modified by Berry phases,…
We discuss a general diagnosis scheme for topological nodal lines protected by time-reversal symmetry and space-inversion symmetry, in the absence of spin-orbit coupling. It is shown that when a shallow band inversion (with a small inverted…