Related papers: Band Connectivity for Topological Quantum Chemistr…
The rich physics of magic angle twisted bilayer graphene (TBG) results from the Coulomb interactions of electrons in flat bands of non-trivial topology. While the bands' dispersion is well characterized, accessing their topology remains an…
Recently it has been found numerically that the spectra of metamaterial crystals may contain pairs of bands which disappear inside the Brillouin zone. We observe that the wave equations for such systems are essentially non-Hermitian, but PT…
The tensionless limit of classical string theory may be formulated as a topological theory on the world-sheet. A vector density carries geometrical information in place of an internal metric. It is found that path-integral quantization…
A full selfconsistent set of equations is deduced to describe the kinetics and dynamics of charged quasiparticles (electrons, holes etc.) with arbitrary dispersion law in crystalline solids subjected to time-varying deformations. The set…
Materials science and the study of the electronic properties of solids are a major field of interest in both physics and engineering. The starting point for all such calculations is single-electron, or non-interacting, band structure…
We show that the electronic structure of the low-energy bands in the small angle-twisted bilayer graphene consists of a series of semi-metallic and topological phases. In particular we are able to prove, using an approximate low-energy…
Most complex systems can be captured by graphs or networks. Networks connect nodes (e.g.\ neurons) through edges (synapses), thus summarizing the system's structure. A popular way of interrogating graphs is community detection, which…
To realize band structures with non-trivial topological properties in an optical lattice is an exciting topic in current studies on ultra cold atoms. Here we point out that this lofty goal can be achieved by using a simple scheme of shaking…
In this work we show that given a connectivity graph $G$ of a $[[n,k,d]]$ quantum code, there exists $\{K_i\}_i, K_i \subset G$, such that $\sum_i |K_i|\in \Omega(k), \ |K_i| \in \Omega(d)$, and the $K_i$'s are $\tilde{\Omega}(…
Grain boundaries in extremely confined colloidal smectics possess a topological fine structure with coexisting nematic and tetratic symmetry of the director field. An alternative way to approach the problem of smectic topology is via the…
We investigate optimal band structures in band-converged systems to achieve high zT using numerical calculations based on a virtual spectral conductivity model. We consider a two parabolic band system, in which multiple band parameters can…
Graph rigidity theory studies the capability of a graph embedded in the Euclidean space to constrain its global geometric shape via local constraints among nodes and edges, and has been widely exploited in network localization and formation…
This paper describes a new approach to the problem of the structural research of clusters based on the theory of geodetic and k-geodetic graphs. We firmly believe that this same approach can be used when solving problems of correlation…
We describe recent progress in our understanding of the interplay between interactions, symmetry, and topology in states of quantum matter. We focus on a minimal generalization of the celebrated topological band insulators to interacting…
We derive a framework for classifying topological bands in three-dimensional photonic band structures, where the zero frequency polarization singularity implied by Maxwell's equations complicates the direct application of existing…
We elucidate the general rule governing the response of dislocation lines in three-dimensional topological band insulators. According to this ${\bf K}\text{-}{\bf b}\text{-}{\bf t}$ rule, the lattice topology, represented by dislocation…
The vacuum of a band system, with respect to particles or holes, can become topologically nontrivial when the exceptional points of the non-hermitian Hamiltonian spread over the whole Brillouin zone. The coalescence of the eigenstates…
The purpose of this paper is to discuss how topology and geometry provide, in many instances, the connective tissue that enables logical comprehension. We illustrate this theme with many examples including Venn diagrams, knot diagrams,…
We uncover the very rich graph topology of generic bounded non-Hermitian spectra, distinct from the topology of conventional band invariants and complex spectral winding. The graph configuration of complex spectra are characterized by the…
Flat bands - single-particle energy bands - in tight-binding networks have attracted attention due to the presence of macroscopic degeneracies and their extreme sensitivity to perturbations. This makes them natural candidates for emerging…