Topological electronic bands in crystalline solids
arXiv:2307.16258 · doi:10.1080/00107514.2023.2251764
Abstract
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 the field. I begin by outlining the relevant concepts from topology, then give a summary of the theory of non-interacting electrons in periodic potentials. Next, I explain the concepts of the Berry phase and Berry curvature, and derive key formulae. The remainder of the article deals with how these ideas are applied to classify crystalline solids according to the topology of the electronic states, and the implications for observable properties. Among the topics covered are the role of symmetry in determining band degeneracies in momentum space, the Chern number and Z2 topological invariants, surface electronic states, two- and three-dimensional topological insulators, and Weyl and Dirac semimetals
A pedagogical review aimed at researchers who are new to the field. Comments and corrections welcome
References in corpus (19)
- The electronic properties of graphene
- Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
- Non-Abelian Anyons and Topological Quantum Computation
- Quantum Spin Hall Insulator State in HgTe Quantum Wells
- Superconducting proximity effect and Majorana fermions at the surface of a topological insulator
- Discovery (theoretical prediction and experimental observation) of a large-gap topological-insulator class with spin-polarized single-Dirac-cone on the surface
- A topological Dirac insulator in a quantum spin Hall phase : Experimental observation of first strong topological insulator
- Topological Field Theory of Time-Reversal Invariant Insulators
- Three dimensional topological invariants for time reversal invariant Hamiltonians and the three dimensional quantum spin Hall effect
- Dirac materials
- Topological nodal line semimetals
- Antiferromagnetic topological insulators
- Progress and prospects in magnetic topological materials
- Axion Electrodynamics in Topological Materials
- Dirac and Weyl Materials: Fundamental Aspects and Some Spintronics Applications
- Topological and geometrical aspects of band theory
- Manifestations of topological effects in graphene
- Skyrmions in magnetic materials
- Magnetic and electronic structure of the topological semimetal YbMnSb