Algebra of Hyperbolic Band Theory under Magnetic Field

• URL: http://arxiv.org/abs/2107.10586v3
• Date: Mon, 29 May 2023 20:05:43 GMT
• Title: Algebra of Hyperbolic Band Theory under Magnetic Field
• Authors: Kazuki Ikeda, Yoshiyuki Matsuki, Shoto Aoki
• Abstract summary: We explore algebras associated with the hyperbolic band theory under a magnetic field for the first time. By imposing the magnetic boundary conditions for the hyperbolic Bloch states, we construct the hyperbolic magnetic Bloch states and investigate their energy spectrum. 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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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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