相关论文: Computing topological invariants without inversion…

We study topological insulators, regarded as physical systems giving rise to topological invariants determined by symmetries both linear and anti-linear. Our perspective is that of noncommutative index theory of operator algebras. In…

We explore the 32 crystallographic point groups and identify topological phases of matter with robust surface modes. For n =3,4 and 6 of the C_{nv} groups, we find the first-known 3D topological insulators without spin-orbit coupling, and…

We present an efficient method for finding the independent invariant tensors of a gauge theory. Our method uses a theorem relating invariant tensors and D-flat directions in field space. We apply our method to several examples-- SO(3) with…

Many magnetic point-group symmetries induce a topological classification on crystalline insulators, dividing them into those that have a nonzero quantized Chern-Simons magnetoelectric coupling ("axion-odd" or "topological"), and those that…

We present practical and formal methods for gauging non-invertible symmetries in (2+1)d topological quantum field theories. Along the way, we generalize various aspects of invertible 0-form gauging, including symmetry fractionalization,…

We propose an experimental technique for classifying the topology of band structures realized in optical lattices, based on a generalization of topological charge pumping in quantum Hall systems to cold atom in optical lattices.…

Transfer matrix methods and intersection theory are used to calculate the bands of edge states for a wide class of periodic two-dimensional tight-binding models including a sublattice and spin degree of freedom. This allows to define…

Two-dimensional (2D) topological electronic insulators are known to give rise to gapless edge modes, which underlie low energy dynamics, including electrical and thermal transport. This has been thoroughly investigated in the context of…

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…

One of the hallmarks of topological insulators is the correspondence between the value of its bulk topological invariant and the number of topologically protected edge modes observed in a finite-sized sample. This bulk-boundary…

Topological invariants are crucial for characterizing topological systems. However, experimentally measuring them presents a significant challenge, especially in non-Hermitian systems where the biorthogonal eigenvectors are often necessary.…

We argue that various kinds of topological insulators (TIs) can be insightfully characterized by an inspection of the charge centers of the hybrid Wannier functions, defined as the orbitals obtained by carrying out a Wannier transform on…

We present a method for computing the classification groups of topological insulators and superconductors in the presence of $\mathbb{Z}_2^{\times n}$ point group symmetries, for arbitrary natural numbers $n$. Each symmetry class is…

We show that compositions of time-reversal and spatial symmetries, also known as the magnetic-space-group symmetries, protect topological invariants as well as surface states that are distinct from those of all preceding topological states.…

We develop a technique for constructing Bloch-like functions for 2D Z_2-insulators (i.e., quantum spin-Hall insulators) that are smooth functions of k on the entire Brillouin-zone torus. As the initial step, the occupied subspace of the…

Following the centuries old concept of the quantization of flux through a Gaussian curvature (Euler characteristic) and its successive dispersal into various condensed matter properties such as quantum Hall effect, and topological…

Based on a recently developed framework, we conduct classifications of time-reversal symmetric topological superconductors with conventional pairing symmetries. Our real-space approach clarifies the nature of boundary modes in nontrivial…

Many advancements have been made in the field of topological mechanics. The majority of the works, however, concerns the topological invariant in a linear theory. We, in this work, present a generic prescription of defining topological…

We survey various quantized bulk physical observables in two- and three-dimensional topological band insulators invariant under translational symmetry and crystallographic point group symmetries (PGS). In two-dimensional insulators, we show…

Topological insulators [1-6] is a new quantum phase of matter with exotic properties such as dissipationless transport and protection against Anderson localization [7]. These new states of quantum matter could be one of the missing links…