相关论文: Band-Structure-Independent Topology from Nonsymmor…

We study one-dimensional disordered systems with average non-invertible symmetries, where quenched disorder may locally break part of the symmetry while preserving it upon disorder averaging. A canonical example is the random…

The explicit construction of non-dispersive flat band modes and the tunability of has been reported for a hierarchical 3-simplex fractal geometry. A single band tight binding Hamiltonian defined for the deterministic self-similar…

We characterize non-Hermitian band structures by symmetry indicator topological invariants. Enabled by crystalline inversion symmetry, these indicators allow us to short-cut the calculation of conventional non-Hermitian topological…

While topology can impose obstructions to exponentially localized Wannier functions, certain topological insulators are exempt from such Wannier obstructions. The absence of the Wannier obstructions can further accompany topological…

The fundamental building blocks in band theory are band representations (BRs): bands whose infinitely-numbered Wannier functions are generated (by action of a space group) from a finite number of symmetric Wannier functions centered on a…

We develop the topological band theory for systems described by non-Hermitian Hamiltonians, whose energy spectra are generally complex. After generalizing the notion of gapped band structures to the non-Hermitian case, we classify "gapped"…

Topological semimetal states which are constrained by symmetries and give birth to innovative excitations are the frontiers of topological quantum matter. Nodal chains in which two nodal rings connect at one point were first discovered in…

The interplay between topology and nonlinearity represents a central challenge in modern physics. Here, we investigate this interplay by considering a synthetic Su-Schrieffer-Heeger lattice with all-to-all nonlocal interactions. We find…

We study non-interacting electrons in disordered materials which exhibit a spectral gap, in each of the ten Altland--Zirnbauer symmetry classes, in all space dimensions. We define an appropriate space of Hamiltonians and a topology on it so…

Crystal symmetries can enforce all bands of a material to be topological, a property that is commonly referred to as ``supertopology". Here, we determine the symmetry-enforced $\mathbb{Z}_2$ supertopologies of non-magnetic centrosymmetric…

It was recently demonstrated that the connectivities of bands emerging from zero frequency in dielectric photonic crystals are distinct from their electronic counterparts with the same space groups. We discover that, in an AB-layer-stacked…

Band theory provides the foundation for understanding electronic structure in crystalline materials, but its reliance on exact translational symmetry limits its applicability to systems with defects, disorder, incommensurate modulations, or…

A powerful result of topological band theory is that nontrivial phases manifest obstructions to constructing localized Wannier functions. In Chern insulators, it is impossible to construct Wannier functions that respect translational…

Band structures of electrons in a periodic potential are well-known to host topologies that impact their behaviors at edges and interfaces. The concept however is more general than the single-electron setting. In this work, we consider…

Space group theory is pivotal in the design of nanophotonics devices, enabling the characterization of periodic optical structures such as photonic crystals. The aim of this study is to extend the application of nonsymmorphic space groups…

Field theories compactified on non-simply connected spaces, which in general allow to impose twisted boundary conditions, are found to unexpectedly have a rich phase structure. One of characteristic features of such theories is the…

Topological invariants are a significant ingredient in the study of topological phases of matter that intertwines the supposedly contradicting concepts of bulk and boundary. The nature of the invariants differ depending on the dimension of…

Topological superconductivity hosts protected quasiparticles and is central to topological quantum computation, yet its realization in intrinsic materials remains challenging and often relies on engineered platforms. Here we uncover a…

Let L be a Schroedinger operator with periodic magnetic and electric potentials, a Maxwell operator in a periodic medium, or an arbitrary self-adjoint elliptic linear partial differential operator in R^n with coefficients periodic with…

The intense theoretical and experimental interest in topological insulators and semimetals has established band structure topology as a fundamental material property. Consequently, identifying band topologies has become an important, but…