相关论文: Topologically coupled energy bands in molecules

Topology is a central notion in the classification of band insulators and characterization of entangled many-body quantum states. In some cases, it manifests as quantized observables such as quantum Hall conductance. However, being…

We study the properties of the quantum states in the one-dimensional system with a shifted periodic potential in both the discrete model and the continuous model. With open boundary conditions, the edge states appear in the energy gaps…

In this Article we address the definition and values of topological numbers of the manifolds of wavefunctions - bands obtained by quantum superposition of the wavefunctions that belong to topologically distinct manifolds. The problem,…

In a flat band superconductor, bosonic excitations can disperse while unpaired electrons are immobile. To study this strongly interacting system, we construct a family of multi-band Hubbard models with exact eta-pairing ground states in all…

The Atiyah-Singer index theorem is a topological formula for the index of an elliptic differential operator. The topological index depends on a cohomology class that is constructed from the principal symbol of the operator. On contact…

The redistribution of energy levels between energy bands is studied for a family of simple effective Hamiltonians depending on one control parameter and possessing axial symmetry and energy-reflection symmetry. Further study is made on the…

The interplay between symmetry and topology leads to a rich variety of electronic topological phases, protecting states such as the topological insulators and Dirac semimetals. Previous results, like the Fu-Kane parity criterion for…

The application of topology, a branch of mathematics, to the study of electronic states in crystalline materials has had a revolutionary impact on the field of condensed matter physics. For example, the development of topological band…

We define generalized Atiyah-Patodi-Singer boundary conditions of product type for Dirac operators associated to C*-vector bundles on the product of a compact manifold with boundary and a closed manifold. We prove a product formula for the…

One of the hallmarks of topological insulators is the correspondence between the value of its bulk topological invariant and the number of topologically protected edge modes observed in a finite-sized sample. This bulk-boundary…

Qualitatively different systems of molecular energy bands are studied on example of a parametric family of effective Hamiltonians describing rotational structure of triply degenerate vibrational state of a cubic symmetry molecule. The…

The conventional theory of solids is well suited to describing band structures locally near isolated points in momentum space, but struggles to capture the full, global picture necessary for understanding topological phenomena. In part of a…

In this talk, we review the heat kernel approach to the Atiyah-Singer index theorem for Dirac operators on closed manifolds, as well as the Atiyah-Patodi-Singer index theorem for Dirac operators on manifolds with boundary. We also discuss…

Topology is now securely established as a means to explore and classify electronic states in crystalline solids. This review provides a gentle but firm introduction to topological electronic band structure suitable for new researchers in…

This paper reviews recent work on a new geometric object called a bundle gerbe and discusses some new examples arising in quantum field theory. One application is to an Atiyah-Patodi-Singer index theory construction of the bundle of…

Quantum metrology is deeply connected to quantum geometry, through the fundamental notion of quantum Fisher information. Inspired by advances in topological matter, it was recently suggested that the Berry curvature and Chern numbers of…

The Atiyah-Singer index theorem gives a topological formula for the index of an elliptic differential operator. Enlightening from Alain Connes' tangent groupoid proof of the index theorem and van Erp's research for the Heisenberg index…

We demonstrate the realization of topological band structures by exploiting the intrinsic spin-orbit coupling of dipolar interactions in combination with broken time-reversal symmetry. The system is based on polar molecules trapped in a…

Topological principles constitute at present an integral component of condensed matter physics, permeating the modern characterization of electronic states while also guiding materials design. In this brief Perspective, I highlight three…

The unique properties of spin-polarized surface or edge states in topological insulators (TIs) make these quantum coherent systems interesting from the point of view of both fundamental physics and their implementation in low power…