TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhys.17.5.124
TI  - Topological linear response of hyperbolic Chern insulators
PY  - 2024/11/04
UR  - https://scipost.org/SciPostPhys.17.5.124
JF  - SciPost Physics
JA  - SciPost Phys.
VL  - 17
IS  - 5
SP  - 124
A1  - Sun, Canon
AU  - Chen, Anffany
AU  - Bzdusek, Tomas
AU  - Maciejko, Joseph
AB  - We establish a connection between the electromagnetic Hall response and band topological invariants in hyperbolic Chern insulators by deriving a hyperbolic analog of the Thouless-Kohmoto-Nightingale-den Nijs (TKNN) formula. By generalizing the Kubo formula to hyperbolic lattices, we show that the Hall conductivity is quantized to $-e^2C_{ij}/h$, where $C_{ij}$ is the first Chern number. Through a flux-threading argument, we provide an interpretation of the Chern number as a topological invariant in hyperbolic band theory. We demonstrate that, although it receives contributions from both Abelian and non-Abelian Bloch states, the Chern number can be calculated solely from Abelian states, resulting in a tremendous simplification of the topological band theory. Finally, we verify our results numerically by computing various Chern numbers in the hyperbolic Haldane model.
ER  -

@Article{10.21468/SciPostPhys.17.5.124,
	title={{Topological linear response of hyperbolic Chern insulators}},
	author={Canon Sun and Anffany Chen and Tomáš Bzdušek and Joseph Maciejko},
	journal={SciPost Phys.},
	volume={17},
	pages={124},
	year={2024},
	publisher={SciPost},
	doi={10.21468/SciPostPhys.17.5.124},
	url={https://scipost.org/10.21468/SciPostPhys.17.5.124},
}