TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhys.15.4.129
TI  - Quantized Berry winding from an emergent $\mathcal{PT}$ symmetry
PY  - 2023/10/03
UR  - https://www.scipost.org/SciPostPhys.15.4.129
JF  - SciPost Physics
JA  - SciPost Phys.
VL  - 15
IS  - 4
SP  - 129
A1  - Louvet, Thibaud
AU  - Delplace, Pierre
AU  - Goerbig, Mark-Oliver
AU  - Carpentier, David
AB  - 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.
ER  -

@Article{10.21468/SciPostPhys.15.4.129,
	title={{Quantized Berry winding from an emergent $\mathcal{PT}$ symmetry}},
	author={Thibaud Louvet and Pierre Delplace and Mark-Oliver Goerbig and David Carpentier},
	journal={SciPost Phys.},
	volume={15},
	pages={129},
	year={2023},
	publisher={SciPost},
	doi={10.21468/SciPostPhys.15.4.129},
	url={https://scipost.org/10.21468/SciPostPhys.15.4.129},
}