Topological linear response of hyperbolic Chern insulators

• URL: http://arxiv.org/abs/2406.08388v1
• Date: Wed, 12 Jun 2024 16:38:43 GMT
• Title: Topological linear response of hyperbolic Chern insulators
• Authors: Canon Sun, Anffany Chen, Tomáš Bzdušek, Joseph Maciejko,
• Abstract summary: We show that the Hall conductivity is quantized to $e2C_ij/h$, where $C_ij$ is the first Chern number. 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.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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