Related papers: Higher-order topological band structures
In crystalline systems with a superstructure, the electron dispersion can form a nontrivial covering of the Brillouin zone. It is proved that the number of sheets in this covering and its monodromy are topological invariants under ambient…
Second-order topological insulators and superconductors have a gapped excitation spectrum in bulk and along boundaries, but protected zero modes at corners of a two-dimensional crystal or protected gapless modes at hinges of a…
By analogy with the formation of space crystals, crystalline structures can also appear in the time domain. While in the case of space crystals we often ask about periodic arrangements of atoms in space at a moment of a detection, in time…
Protection of topological surface states by reflection symmetry breaks down when the boundary of the sample is misaligned with one of the high symmetry planes of the crystal. We demonstrate that this limitation is removed in amorphous…
This note is a survey on the topology of hyperplane arrangements. We mainly focus on the relationship between topology and the real structure, such as adjacent relations of chambers and stratifications related to real structures.
The study of spatial symmetries was accomplished during the last century, and had greatly improved our understanding of the properties of solids. Nowadays, the symmetry data of any crystal can be readily extracted from standard…
Topological phases stabilized by crystalline point group symmetry protection are a large class of symmetry-protected topological phases subjected to considerable experimental scrutiny. Here, we show that the canonical three-dimensional (3D)…
The recent discovery and realizations of higher-order topological insulators enrich the fundamental studies on topological phases. Here, we report three-dimensional (3D) wave-steering capabilities enabled by topological boundary states at…
We investigate higher-order topological states in honeycomb lattice with Y-Kekul\'e distortions that preserve $C_{6v}$ crystalline symmetry. The gapped states in expanded and shrunken distortions are adiabatically connected to isolated…
In crystalline systems, higher-order topology, characterized by topological states of codimension greater than one, typically arises from the mismatch between Wannier centers and atomic sites, leading to filling anomalies. However, this…
Previous symmetry-based database searches have already revealed ubiquitous band topology in nature, while the destiny of band topology under symmetry-breaking is yet to be studied comprehensively. Here we first develop a framework allowing…
In recent years, there has been a surge of interest in higher-order topological phases (HOTPs) across various disciplines within the field of physics. These unique phases are characterized by their ability to harbor topological protected…
Topological crystalline insulators are new states of matter in which the topological nature of electronic structures arises from crystal symmetries. Here we predict the first material realization of topological crystalline insulator in the…
The study of topology in solids is undergoing a renaissance following renewed interest in the properties of ferroic domain walls as well as recent discoveries regarding topological insulators and skyrmionic lattices. Each of these systems…
Topological band insulators (TBIs) are bulk insulating materials which feature topologically protected metallic states on their boundary. The existing classification departs from time-reversal symmetry, but the role of the crystal lattice…
By developing a generalized cobordism theory, we explore the higher global symmetries and higher anomalies of quantum field theories and interacting fermionic/bosonic systems in condensed matter. Our essential math input is a generalization…
Symmetry protected topological (SPT) phases of bosons in $d$ spatial dimensions have been characterized by the action of the protecting global symmetry $G$ on their boundary. The symmetry acts on the boundary in a way that would be…
Recent years saw the complete classification of topological band structures, revealing an abundance of topological crystalline insulators. Here we theoretically demonstrate the existence of topological materials beyond this framework,…
The past decade's apparent success in predicting and experimentally discovering distinct classes of topological insulators (TIs) and semimetals masks a fundamental shortcoming: out of 200,000 stoichiometric compounds extant in material…
We present a method for efficiently enumerating all allowed, topologically distinct, electronic band structures within a given crystal structure. The algorithm applies to crystals with broken time-reversal, particle-hole, and chiral…