相关论文: A real-space many-body marker for correlated ${\ma…
Anderson's localization on the edge of two dimensional time reversal (TR) topological insulator (TI) is studied. For the non-interacting case the topological protection acts accordingly to the $\mathbb{Z}_2$ classification, leading to…
We propose a topological order parameter for interacting topological insulators, expressed in terms of the full Green's functions of the interacting system. We show that it is exactly quantized for a time reversal invariant topological…
In this paper topological $K$-group calculations for fiber bundles with structure group $SO(3)$ over tori are carried out to explain why topological insulators have special conducting points on their surface but are bulk insulators. It is…
We investigate the three-dimensional, time-reversal invariant topological superconductors with generic interaction by their response to external fields. The first description is a gravitational topological field theory, which gives a $Z_2$…
We study the edge and surface theories of topological insulators from the perspective of anomalies and identify a novel Z2-anomaly associated with charge conservation. The anomaly is manifested through a 2-point correlation function…
We define topological invariants in terms of the ground states wave functions on a torus. This approach leads to precisely defined formulas for the Hall conductance in four dimensions and the topological magneto-electric $\theta$ term in…
We discuss a topological classification of insulators and superconductors in the presence of both (non-spatial) discrete symmetries in the Altland-Zirnbauer classification and spatial reflection symmetry in any spatial dimensions. By using…
Topological insulators have become one of the most active research areas in condensed matter physics. This article reviews progress on the topic of electronic correlations effects in the two-dimensional case, with a focus on systems with…
We study effect of interactions on time-reversal-invariant topological insulators. Their topological indices are expressed by interacting Green's functions. Under the local self-energy approximation, we connect topological index and surface…
We propose a new method to numerically compute the $\mathbb{Z}_2$ indices for disordered topological insulators in Kitaev's periodic table. All of the $\mathbb{Z}_2$ indices are known to be derived from the index formulae which are…
The relation between bulk topological invariants and experimentally observable physical quantities is a fundamental property of topological insulators and superconductors. In the case of chiral symmetric systems in odd spatial dimensions…
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…
We systematically study topological phases of insulators and superconductors (SCs) in 3D. We find that there exist 3D topologically non-trivial insulators or SCs in 5 out of 10 symmetry classes introduced by Altland and Zirnbauer within the…
This paper reviews recent results on the classification of partial differential operators modeling bulk and interface topological insulators in Euclidean spaces. Our main objective is the mathematical analysis of the unusual,…
In a basic framework of a complex Hilbert space equipped with a complex conjugation and an involution, linear operators can be real, quaternionic, symmetric or anti-symmetric, and orthogonal projections can furthermore be symplectic. This…
The role of disorder in the field of three-dimensional time reversal invariant topological insulators has become an active field of research recently. However, the computation of Z2 invariants for large, disordered systems still poses a…
A fundamental open problem in condensed matter physics is how the dichotomy between conventional and topological band insulators is modified in the presence of strong electron interactions. We show that there are 6 new electronic…
We develop a theory of the correlated magnetically ordered insulating state at the edge of a two-dimensional topological insulator. We demonstrate that the gapped spin-polarized state, induced by the application of the magnetic field $B$,…
The topological phases of two-dimensional time-reversal symmetric insulators are classified by a $\mathbb{Z}_{2}$ topological invariant. Usually, the invariant is introduced and calculated by exploiting the way time-reversal symmetry acts…
We introduce a general scheme for constructing order parameters (OPs) by extracting generic patterns from the dominant Fock states of many-body ground states. While topological phases are traditionally characterized by non-local invariants,…