相关论文: Comment on ``Near-field spin Chern number quantize…

The Chern number has been widely used to describe the topological properties of periodic structures in the momentum space. Here, we introduce a real-space spin Chern number for the optical near fields of finite-sized structures. This new…

The index theorem of Euler-Poincar\'e characteristic of manifold with boundary is given by making use of the general decomposition theory of spin connection. We shows the sum of the total index of a vector field $\phi $ and half the total…

We obtain the band structure of a particle moving in a magnetic spin texture, classified by its chirality and structure factor, in the presence of spin-orbit coupling. This rich interplay leads to a variety of novel topological phases…

In two-dimensional time-reversal symmetric topological insulators described by Dirac models, the ${\mathbb Z}_{2}$ topological invariant can be described by the spin Chern number. We present a linear response theory for the spin Berry…

We study the ground-state topology and quasiparticle properties in bosonic Mott insulators with two- dimensional spin-orbit couplings in cold atomic optical lattices. We show that the many-body Chern and spin-Chern number can be expressed…

Chern number is usually characterized by Berry curvature. Here, by investigating the Dirac model of even-dimensional Chern insulator, we give the general relation between Berry curvature and quantum metric, which indicates that the Chern…

Berry curvature is a fundamental element to characterize topological quantum physics, while a full measurement of Berry curvature in momentum space was not reported for topological states. Here we achieve two-dimensional Berry curvature…

We propose two thermo-spintronic responses in proximity induced superconductors with spin-orbit coupled band - spin Nernst effect and thermal Edelstein effect stemming respectively from momentum-space and mixed superconducting Berry…

Berry curvature that describes local geometrical properties of energy bands can elucidate many fascinating phenomena in solid-state, photonic, and phononic systems, given its connection to global topological invariants such as the Chern…

We generalize the concept of topological invariants for mixed states based on the ensemble geometric phase (EGP) introduced for one-dimensional lattice models to two dimensions. In contrast to the geometric phase for density matrices…

The topological structure of the wavefunctions of particles in periodic potentials is characterized by the Berry curvature $\Omega_{kn}$ whose integral on the Brillouin zone is a topological invariant known as the Chern number. The…

We present a manifestly gauge-invariant description of Chern numbers associated with the Berry connection defined on a discretized Brillouin zone. It provides an efficient method of computing (spin) Hall conductances without specifying…

We show that assuming lower bounds on the Ricci curvature and the injectivity radius the absolute value of certain characteristic numbers of a Riemannian manifold, including all Pontryagin and Chern numbers, is bounded proportionally to the…

For the moduli spaces of Abelian differentials, the Euler characteristic is one of the most basic intrinsic topological invariants. We give a formula for the Euler characteristic that relies on intersection theory on the smooth…

The Chern topological numbers of a material system are traditionally written in terms of the Berry curvature which depends explicitly on the material band structure and on the Bloch eigenwaves. Here, we demonstrate that it is possible to…

If an extensive partition in two dimensions yields a gapful entanglement spectrum of the reduced density matrix, the Berry curvature based on the corresponding entanglement eigenfunction defines the Chern number. We propose such an…

Topological invariants such as winding numbers and linking numbers appear as charges of topological solitons in diverse nonlinear physical systems described by a unit vector field defined on two and three dimensional manifolds. While the…

We prove a discrete Gauss-Bonnet-Chern theorem which states where summing the curvature over all vertices of a finite graph G=(V,E) gives the Euler characteristic of G.

The sphere formula states that in an arbitrary finite abstract simplicial complex, the sum of the Euler characteristic of unit spheres centered at even-dimensional simplices is equal to the sum of the Euler characteristic of unit spheres…

The geometry and topology of quantum systems have deep connections to quantum dynamics. In this paper, I show how to measure the non-Abelian Berry curvature and its related topological invariant, the second Chern number, using dynamical…