Related papers: $\mathbb{Z}_2$ topological invariants from the Gre…
The purpose of this paper is to study transport equations on the unit tangent bundle of closed oriented Riemannian surfaces and to connect these to the transport twistor space of the surface (a complex surface naturally tailored to the…
A Green's function formalism is used to calculate the spectrum of excitations of two neighboring impurities implanted in a semi-infinite ferromagnetic. The equations of motion for the Green's functions are determined in the framework of the…
We explore a large family of one-dimensional (1D) topological crystalline insulators (TCIs) classified by $\mathbb{Z}$ invariants protected by space-time inversion symmetry. This finding stands in marked contrast to the conventional…
We report intimate relations between topological properties of full gapped spin-triplet superconductors with time-reversal invariance and the Fermi surface topology in the normal states. An efficient method to calculate the Z2 invariants…
We present a fully many-body formulation of topological invariants for various topological phases of fermions protected by antiunitary symmetry, which does not refer to single particle wave functions. For example, we construct the many-body…
We investigate the effects of magnetic and nonmagnetic impurities on the two-dimensional surface states of three-dimensional topological insulators (TIs). Modeling weak and strong TIs using a generic four-band Hamiltonian, which allows for…
Symmetries play an essential role in identifying and characterizing topological states of matter. Here, we classify topologically two-dimensional (2D) insulators and semimetals with vanishing spin-orbit coupling using time-reversal…
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…
The unique properties of spin-polarized surface or edge states in topological insulators (TIs) make these quantum coherent systems interesting from the point of view of both fundamental physics and their implementation in low power…
As one of the first proposed topologically protected states, the quantum spin Hall effect in graphene relies critically on the existence of a spin-dependent gap at the K/K' points of the Brillouin zone. Using a tight-binding formulation…
One of the remarkable interaction effects on topological insulators is the reduction of topological classification in free-fermion systems. We address this issue in a bilayer honeycomb lattice model by taking into account temperature…
Topological invariants play a key role in the characterization of topological states. Due to the existence of exceptional points, it is a great challenge to detect topological invariants in non-Hermitian systems. We put forward a dynamic…
In this paper we investigate the $(2+1)$-dimensional topological non-Fermi liquid in strongly correlated electron system, which has a holographic dual description by Einstein gravity in $(3+1)$-dimensional anti-de Sitter (AdS) space-time.…
We propose a many-body generalization of the Z2 topological invariant for the quantum spin Hall insulator, which does not rely on single-particle band structures. The invariant is derived as a topological obstruction that distinguishes…
We propose a simple geometrical construction of topological invariants of 3-strand Brownian braids viewed as world lines of 3 particles performing independent Brownian motions in the complex plane z. Our construction is based on the…
In theory of topological classification, the 2D topological superconductors without time reversal symmetry are characterized by Chern numbers. However, in reality, we find the Chern numbers can not reveal the whole properties of the…
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…
A spin-U(1)-symmetry protected momentum-dependent integer-$Z$-valued topological invariant is proposed to time-reversal-invariant (TRI) superconductivity (SC) whose nonzero value will lead to exactly flat surface band(s). The theory is…
Topological insulators are characterized by a nontrivial band topology driven by the spin-orbit coupling. To fully explore the fundamental science and application of topological insulators, material realization is indispensable. Here we…
A topological flux function is introduced to quantify the topology of magnetic braids: non-zero line-tied magnetic fields whose field lines all connect between two boundaries. This scalar function is an ideal invariant defined on a…