相关论文: Index theory and bulk-boundary correspondence for …

Bulk-edge correspondence is a wide-ranging principle that applies to topological matter, as well as a precise result established in a large and growing number of cases. According to the principle, the distinctive topological properties of…

We study the topology of two-dimensional open systems in terms of the Green's function. The Ishikawa-Matsuyama formula for the integer topological invariant is applied in open systems, which indicates the number difference of gapless edge…

We define certain class of correspondences of polarized representations of $C^*$-algebras. Our correspondences are modeled on the spaces of boundary values of elliptic operators on bordisms joining two manifolds. In this setup we define the…

We show that a slab of a three-dimensional inversion-symmetric higher-order topological insulator (HOTI) in class A is a 2D Chern insulator, and that in class AII is a 2D $Z_2$ topological insulator. We prove it by considering a process of…

The mathematical field of topology has become a framework to describe the low-energy electronic structure of crystalline solids. A typical feature of a bulk insulating three-dimensional topological crystal are conducting two-dimensional…

In this paper, we discuss index theory for Toeplitz operators on a discrete quarter-plane of two-variable rational matrix function symbols. By using Gohberg-Krein theory for matrix factorizations, we extend the symbols defined originally on…

We compare two approaches which use K-theory for C*-algebras to classify symmetry protected topological phases of quantum systems described in the one particle approximation. In the approach by Kellendonk, which is more abstract and more…

Topological crystalline superconductors have attracted rapidly rising attention due to the possibility of higher-order phases, which support Majorana modes on boundaries in $d-2$ or lower dimensions. However, although the classification and…

We find lower bounds on the rank of a "real" vector bundle over an involutive space, such that "real" vector bundles of higher rank have a trivial summand and such that a stable isomorphism for such bundles implies ordinary isomorphism. We…

Consider a pair of symplectic varieties dual with respect to 3D-mirror symmetry. The K-theoretic limit of the elliptic duality interface is an equivariant K-theory class of the product. We show that this class provides correspondences in…

We prove the bulk-edge correspondence in $K$-theory for the quantum Hall effect by constructing an unbounded Kasparov module from a short exact sequence that links the bulk and boundary algebras. This approach allows us to represent bulk…

Unlike broken time-reversal symmetric (TRS) systems with a defined Chern number, directly measuring the bulk $Z_{2}$ invariant and Berry curvature (if nonzero) in topological insulators and their higher-order topological families remains an…

Topological insulators feature a number of topologically protected boundary modes linked to the value of their bulk invariant. While in one-dimensional systems the boundary modes are zero dimensional and localized, in two-dimensional…

We consider a gapped periodic quantum system with time-reversal symmetry of fermionic (or odd) type, i.e. the time-reversal operator squares to -1. We investigate the existence of periodic and time-reversal invariant Bloch frames in…

Topological insulators are insulating in the bulk but feature conducting states on their surfaces. Standard methods for probing their topological properties largely involve probing the surface, even though topological invariants are defined…

Floquet topological insulators describe independent electrons on a lattice driven out of equilibrium by a time-periodic Hamiltonian, beyond the usual adiabatic approximation. In dimension two such systems are characterized by integer-valued…

In this article, we start to recall the inversion formula for the convolution with the Box spline. The equivariant cohomology and the equivariant K-theory with respect to a compact torus G of various spaces associated to a linear action of…

Atmospheric and oceanic mass transport near the equator display a well-studied asymmetry characterized by two modes moving eastward. This asymmetric edge transport is characteristic of interfaces separating two-dimensional topological…

This paper analyzes Floquet topological insulators resulting from the time-harmonic irradiation of electromagnetic waves on two dimensional materials such as graphene. We analyze the bulk and edge topologies of approximations to the…

We consider families of theories with large N=4 superconformal symmetry. We define an index generalizing the elliptic genus of theories with N=2 symmetry. In contrast to the N=2 case, the new index constrains part of the non-BPS spectrum.…