Figure - PMC

Skip to main content

An official website of the United States government

Here's how you know

Here's how you know

Official websites use .gov
A .gov website belongs to an official government organization in the United States.

Secure .gov websites use HTTPS
A lock ( ) or https:// means you've safely connected to the .gov website. Share sensitive information only on official, secure websites.

View full-text article in PMC

. 2022 May 4;9(5):1483–1499. doi: 10.1021/acsphotonics.1c01874

Search in PMC
Search in PubMed
View in NLM Catalog
Add to search

© 2022 The Authors. Published by American Chemical Society

Permits the broadest form of re-use including for commercial purposes, provided that author attribution and integrity are maintained (https://creativecommons.org/licenses/by/4.0/).

PMC Copyright notice

Geometric topology and band structures: (a) A local geometry can have positive or negative curvature, K, with respect to a reference point. When integrated over a closed surface, , the Gauss-Bonnet theorem links the curvature of the surface to its genus, g, via the relation ∫KdA = 4π(1 – g). The genus of a sphere is g = 0, and that of a torus is g = 1. (b) Link between geometric topology and band topology. Band structures with gap, crossing, and new gap. (c) Schematic of edge states. Dimensions and flavor of topology in the system dictates the characteristics and the number of edge states expected.

Inline graphic — Geometric topology and band structures: (a) A local geometry can have positive or negative curvature, K, with respect to a reference point. When integrated over a closed surface, , the Gauss-Bonnet theorem links the curvature of the surface to its genus, g, via the relation ∫KdA = 4π(1 – g). The genus of a sphere is g = 0, and that of a torus is g = 1. (b) Link between geometric topology and band topology. Band structures with gap, crossing, and new gap. (c) Schematic of edge states. Dimensions and flavor of topology in the system dictates the characteristics and the number of edge states expected.