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arXiv · 2107.10586

Algebra of Hyperbolic Band Theory under Magnetic Field

Kazuki Ikeda·Yoshiyuki Matsuki·Shoto Aoki
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Abstract

We explore algebras associated with the hyperbolic band theory under a magnetic field for the first time. We define the magnetic Fuchsian group associated with a higher genus Riemann surface. By imposing the magnetic boundary conditions for the hyperbolic Bloch states, we construct the hyperbolic magnetic Bloch states and investigate their energy spectrum. We give a connection between such magnetic Bloch states and automorphic forms. Our theory is a general extension of the conventional algebra associated with the band theory defined on a Euclidean lattice/space into that of the band theory on a general hyperbolic lattice/Riemann surface.

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Kazuki Ikeda, Yoshiyuki Matsuki, Shoto Aoki. 2021-07-22. Algebra of Hyperbolic Band Theory under Magnetic Field. https://doi.org/10.1139/cjp-2022-0145

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