Algebra of Hyperbolic Band Theory under Magnetic Field
arXiv:2107.10586 · doi:10.1139/cjp-2022-0145
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.
arXiv admin note: substantial text overlap with arXiv:2104.13314
References in corpus (8)
- Simulating hyperbolic space on a circuit board
- Observation of novel topological states in hyperbolic lattices
- Automorphic Bloch theorems for hyperbolic lattices
- Hyperbolic Topological Band Insulators
- Chern insulator in a hyperbolic lattice
- Universality of Hofstadter butterflies on hyperbolic lattices
- Hyperbolic Band Theory under Magnetic Field and Dirac Cones on a Higher Genus Surface
- Selberg trace formula in hyperbolic band theory