Related papers: Berry-Chern monopoles and spectral flows
Inserting a magnetic flux into a two-dimensional one-particle Hamiltonian leads to a spectral flow through a given gap which is equal to the Chern number of the associated Fermi projection. This paper establishes a generalization to higher…
Generalized Dirac monopoles in momentum space are constructed in even d+1 dimensions from the Weyl Hamiltonian in terms of Green's functions. In 3+1 spacetime dimensions, the (unit) charge of the monopole is equal to both the winding number…
We study topological properties of families of Hamiltonians which may contain degenerate energy levels aka. band crossings. The primary tool are Chern classes, Berry phases and slicing by surfaces. To analyse the degenerate locus, we study…
Topological Chern indices are related to the number of rotational states in each molecular vibrational band. Modification of the indices is associated to the appearance of ``band degeneracies'', and exchange of rotational states between two…
We report on a study of topological properties of Fibonacci quasicrystals. Chern numbers which label the dense set of spectral gaps, are shown to be related to the underlying palindromic symmetry. Topological and spectral features are…
The winding numbers for the even d+1 spacetime dimensional Weyl Hamiltonians are calculated in terms of the related Green's functions. It is shown that these winding numbers result in the divergence of the Dirac monopole fields, hence they…
Inhomogeneous media commonly support a discrete number of wave modes that are trapped along interfaces defined by spatially varying parameters. When they are robust against continuous deformations of parameters, such waves are said to be of…
Motivated by the geometric character of spin Hall conductance, the topological invariants of generic superconductivity are discussed based on the Bogoliuvov-de Gennes equation on lattices. They are given by the Chern numbers of degenerate…
Topological wave phenomena in continuous media are fundamentally challenged by unbounded spectra and the absence of a compact Brillouin zone, which obstruct conventional bulk--interface formulations. We develop a unified phase-space…
The properties that quantify photonic topological insulators (PTIs), Berry phase, Berry connection, and Chern number, are typically obtained by making analogies between classical Maxwell's equations and the quantum mechanical…
Band topology of anomalous quantum Hall insulators can be precisely addressed by computing Chern numbers of constituent non-degenerate bands that describe quantized, Abelian Berry flux through two-dimensional Brillouin zone. Can Chern…
The Berry connection plays a central role in our description of the geometric phase and topological phenomena. In condensed matter, it describes the parallel transport of Bloch states and acts as an effective "electromagnetic" vector…
Weyl fermions with nonlinear dispersion have appeared in real world systems, such as in the Weyl semi-metals and topological insulators. We consider the most general form of Dirac operators, and study its topological properties embedded in…
In 2D semiconductors and insulators, the Chern number of the valence band Bloch state is an important quantity that has been linked to various material properties, such as the topological order. We elaborate that the opacity of 2D materials…
Topological insulators in odd dimensions are characterized by topological numbers. We prove the well-known relation between the topological number given by the Chern character of the Berry curvature and the Chern-Simons level of the low…
Through understanding Maxwell's equations as an effective Dirac equation (the `optical Dirac equation'), we re--examine the relationship between electromagnetic interface states and topology. We illustrate a simple case where…
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…
Topological band insulators are classified using momentum-space topological invariants, such as Chern or winding numbers, when they feature translational symmetry. The lack of translation symmetry in disordered, quasicrystalline, or…
The study of unconventional phases and elucidation of correspondences between topological invariants and their intriguing properties are pivotal in topological physics. Here, we investigate a complex exceptional ring (CER), composed of a…
Topology is bringing new tools for the study of fluid waves. The existence of unidirectional Yanai and Kelvin equatorial waves has been related to a topological invariant, the Chern number, that describes the winding of $f$-plane shallow…