Related papers: Topological charge conservation for continuous ins…
We discuss the thermal (or gravitational) responses in topological superconductors and in topological phases in general. Such thermal responses (as well as electromagnetic responses for conserved charge) provide a definition of topological…
We propose a many-body index that extends Fredholm index theory to many-body systems. The index is defined for any charge-conserving system with a topologically ordered $p$-dimensional ground state sector. The index is fractional with the…
The static topological fractional charge (TFC) in condensed matter systems is related to the band topology and thus has potential applications in topological quantum computation. However, the experimental measurement of these TFCs in…
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 classify topological insulators and superconductors in the presence of additional symmetries such as reflection or mirror symmetries. For each member of the 10 Altland-Zirnbauer symmetry classes, we have a Clifford algebra defined by…
It has recently been shown that in every spatial dimension there exist precisely five distinct classes of topological insulators or superconductors. Within a given class, the different topological sectors can be distinguished, depending on…
We present a rigorous but elementary index theory for a class of one-dimensional systems of interacting (and possibly disordered) fermions with $\Uone\rtimes\bbZ_2$ symmetry defined on the infinite chain. The class includes the…
Quantum Spin-Hall systems are topological insulators displaying dissipationless spin currents flowing at the edges of the samples. In contradistinction to the Quantum Hall systems where the charge conductance of the edge modes is quantized,…
Spectral measurements of boundary localized in-gap modes are commonly used to identify topological insulators via the bulk-boundary correspondence. This can be extended to high-order topological insulators for which the most striking…
We study the entanglement spectrum (ES) of two-dimensional $C_{n}$-symmetric second-order topological insulators (TIs). We show that some characteristic higher order topological observables, e.g., the filling anomaly and its associated…
The three-dimensional topological insulator (originally called "topological insulators") is the first example in nature of a topologically ordered electronic phase existing in three dimensions that cannot be reduced to multiple copies of…
We analyze generalizations of two dimensional topological insulators which can be realized in interacting, time reversal invariant electron systems. These states, which we call fractional topological insulators, contain excitations with…
The study of topological superconductivity is largely based on the analysis of mean-field Hamiltonians that violate particle number conservation and have only short-range interactions. Although this approach has been very successful, it is…
This paper concerns the $\mathbb{Z}_2$ classification of Fermionic Time-Reversal (FTR) symmetric partial differential Hamiltonians on the Euclidean plane. We consider the setting of two insulators separated by an interface. Hamiltonians…
A central property of (Chern) topological insulators is the presence of robust asymmetric transport along interfaces separating two-dimensional insulating materials in different topological phases. A Topological Anderson Insulator is an…
The hallmark property of two-dimensional topological materials is the incredible robustness of the quantized Hall conductivity to disorder. That robustness arises from the fact that in the topological band gap, transport can occur only…
This paper concerns the asymmetric transport observed along interfaces separating two-dimensional bulk topological insulators modeled by (continuous) differential Hamiltonians and how such asymmetry persists after numerical discretization.…
Topological insulators are exotic material that possess conducting surface states protected by the topology of the system. They can be classified in terms of their properties under discrete symmetries and are characterized by topological…
We rigorously yet concisely prove the bulk-edge correspondence for general $d$-dimensional ($d$D) topological insulators in complex Altland-Zirnbauer classes, which states that the bulk topological number equals to the edge-mode index.…
Topological insulators in three dimensions are characterized by a Z2-valued topological invariant, which consists of a strong index and three weak indices. In the presence of disorder, only the strong index survives. This paper studies the…