Contributor info: Mr Thibaud Louvet

Thibaud Louvet, Pierre Delplace, Mark-Oliver Goerbig, David Carpentier

SciPost Phys. 15, 129 (2023) · published 3 October 2023 | Toggle abstract · pdf

Linear crossings of energy bands occur in a wide variety of materials. In this paper we address the question of the quantization of the Berry winding characterizing the topology of these crossings in dimension $D=2$. Based on the historical example of $2$-bands crossing occuring in graphene, we propose to relate these Berry windings to the topological Chern number within a $D=3$ dimensional extension of these crossings. This dimensional embedding is obtained through a choice of a gap-opening potential. We show that the presence of an (emergent) $\mathcal{PT}$ symmetry, local in momentum and antiunitary, allows the quantization of the Berry windings as multiples of $\pi$. We illustrate this quantization mechanism on a variety of three-band crossings.