Related papers: Topologically coupled energy bands in molecules
Using semi-classical analysis in $\mathbb{R}^{n}$ we present a quite general model for which the topological index formula of Atiyah-Singer predicts a spectral flow with the transition of a finite number of eigenvalues between clusters…
We study a family of pseudodifferential operators (quantum Hamiltonians) on $L^{2}(\mathbb{R}^{n};\mathbb{C}^{d})$ whose spectrum exhibits two energy bands exchanging a finite number of eigenvalues. We show that this number coincides with…
Topological phases play a crucial role in the fundamental physics of light-matter interaction and emerging applications of quantum technologies. However, the topological band theory of waveguide QED systems is known to break down, because…
The past decade's apparent success in predicting and experimentally discovering distinct classes of topological insulators (TIs) and semimetals masks a fundamental shortcoming: out of 200,000 stoichiometric compounds extant in material…
The study of topology of energy bands in solid has always been interesting and fruitful. Historically, Thouless et al proposed the TKNN number or Chern number of the energy bands to explain the quantization of Hall conductance in the…
Topological phases of matter are generally characterized by topological properties of energy bands of a system. Their transitions under preserved symmetries occur through closing a gap of energy bands, leading to topologically protected…
We analyze a tight binding model of two coupled chains with strongly interacting fermions. Depending on the parameter $w$, the many body lowest energy band consists of either single particles or bound pairs. A topological quantum pump can…
In this article, we provide a pedagogical review of the theory of topological quantum chemistry and topological crystalline insulators. We begin with an overview of the properties of crystal symmetry groups in position and momentum space.…
The Atiyah-Singer index theorem, a cornerstone of modern mathematics, has traditionally been derived from supersymmetric (SUSY) physics. This paper demonstrates a direct derivation from non-supersymmetric quantum statistics by establishing…
Topological materials are quantum materials with nontrivial ground-state entanglement that are irremovable so long as certain rules, like invariance under symmetries and the existence of an energy gap, are respected. They showcase…
There have been significant recent advances in realizing bandstructures with geometrical and topological features in experiments on cold atomic gases. We provide an overview of these developments, beginning with a summary of the key…
The quest to realize topological band structures in artificial matter is strongly focused on lattice systems, and only quantum Hall physics is known to appear naturally also in the continuum. In this letter, we present a proposal based on a…
In the research of the topological band phases, the conventional wisdom is to start from the crystalline translational symmetry systems. Nevertheless, the translational symmetry is not always a necessary condition for the energy bands. Here…
On the basis of the "molecular-orbital" representation which describes generic flat-band models, we propose a systematic way to construct a class of flat-band models with finite-range hoppings that have topological natures. In these models,…
We give a cohomological formula for the index of a fully elliptic pseudodifferential operator on a manifold with boundary. As in the classic case of Atiyah-Singer, we use an embedding into an euclidean space to express the index as the…
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…
The electronic bands are classified according to their topology. We compute the connection and curvature for the electronic bands and show that the physical properties are determined by topological invariants which are equivalent to the…
The Atiyah-Singer index theorem, a landmark achievement of the early 1960s, brings together ideas in analysis, geometry, and topology. We recount some antecedents and motivations; various forms of the theorem; and some of its implications,…
The Atiyah-Patodi-Singer index theorem describes the bulk-edge correspondence of symmetry protected topological insulators. The mathematical setup for this theorem is, however, not directly related to the physical fermion system, as it…
A twist between two systems offers the possibility to drastically change the underlying physical properties. To that end, we study the bandstructure of twisted moir\'e potentials in detail. At sets of commensurate twisting angles, the low…