相关论文: Berry-Chern monopoles and spectral flows

In 1954 Hirzebruch asked which linear combinations of Chern numbers are topological invariants of smooth complex projective varieties. We give a complete answer to this question in small dimensions, and also prove partial results without…

We demonstrate that a Weyl point, widely examined in 3D Weyl semimetals and superfluids, can develop a pair of non-degenerate gapless spheres. Such a bouquet of two spheres is characterized by three distinct topological invariants of…

The a-function is a proposed quantity defined for quantum field theories which has a monotonic behaviour along renormalisation group flows, being related to the beta-functions via a gradient flow equation involving a positive definite…

Chern number is a crucial invariant for characterizing topological feature of two-dimensional quantum systems. Real-space Chern number allows us to extract topological properties of systems without involving translational symmetry, and…

Previously, it was believed that conduction and valence bands exhibit a symmetry: They possess opposite topological invariants (e.g., the Chern numbers of conduction and valence bands for the Chern insulator are $\pm C$). However, we…

Topological insulator-based methods underpin the topological classification of gapped bands, including those surrounding semi-metallic nodal defects. However, multiple bands with gap-closing points can also possess non-trivial topology. We…

The Leray-Serre and the Eilenberg-Moore spectral sequences are fundamental tools for computing the cohomology of a group or, more generally, of a space. We describe the relationship between these two spectral sequences when both of them…

We discuss methods for calculating Chern numbers of two-dimensional lattice systems using spiral boundary conditions, which sweep all lattice sites in one-dimensional order. Specifically, we establish the one-dimensional representation of…

The spectra of parallel flows (that is, flows governed by first-order differential operators parallel to one direction) are investigated, on both $L^2$ spaces and weighted-$L^2$ spaces. As a consequence, an example of a flow admitting a…

The method of resurgent continuation of transseries reveals a new correspondence between the $q$-series for enumerating degeneracies of quarter-BPS states in supersymmetric black holes and $\hat{Z}$ invariants of Chern-Simons theory on a…

We consider systems described by the two-dimensional Dirac equation where the Fermi velocity is inhomogeneous as a consequence of mechanical deformations. We show that the mechanical deformations can lead to deflection and focusing of the…

The organization of the electrons in the ground state is classified by means of topological invariants, defined as global properties of the wavefunction. Here we address the Chern number of a two-dimensional insulator and we show that the…

Statistical Topology emerged since topological aspects continue to gain importance in many areas of physics. It is most desirable to study topological invariants and their statistics in schematic models that facilitate the identification of…

In this paper we show that the Chern numbers of a smooth Mori fibre space in dimension three are bounded in terms of the underlying topological manifold. We also generalise a theorem of Cascini and the second named author on the boundedness…

We consider SU(N) Yang-Mills theories in 2n+1 Euclidean dimensions coupled to an even flavour-number of Dirac fermions. After integrating out the fermions the wave functional for the effective Yang-Mills theory inherits a non-trivial…

Topological insulators are substances which are bulk insulators but which carry current via special "topologically protected" edge states. The understanding of long range topological order in these systems is built around the idea of a…

Topology ultimately unveils the roots of the perfect quantization observed in complex systems. The 2D quantum Hall effect is the celebrated archetype. Remarkably, topology can manifest itself even in higher-dimensional spaces in which…

We study a new class of topological charge density wave states exhibiting monopole harmonic symmetries. The density-wave ordering is equivalent to pairing in the particle-hole channel due to Fermi surface nesting under interactions. When…

We study the behaviour of Chern numbers of three dimensional terminal varieties under divisorial contractions.

We generalize the concept of Berry connection of the single-electron band structure to the two-particle Cooper pair states between two Fermi surfaces with opposite Chern numbers. Because of underlying Fermi surface topology, the pairing…