Fuerst, Maximilian and Kochan, Denis and Dusa, Ioachim-Gheorghe and Gorini, Cosimo and Richter, Klaus (2024) Dirac Landau levels for surfaces with constant negative curvature. PHYSICAL REVIEW B, 109 (19): 195433. ISSN 2469-9950, 2469-9969
Full text not available from this repository.Abstract
Studies of the formation of Landau levels based on the Schr & ouml;dinger equation for electrons constrained to curved surfaces have a long history. These include as prime examples surfaces with constant negative curvature, like the pseudosphere [A. Comtet, Ann. Phys. 173 , 85 (1987)]. Now, topological insulators, hosting Dirac -type surface states, provide a unique platform to experimentally examine such quantum Hall physics in curved space. Hence, extending previous work we consider solutions of the Dirac equation for the pseudosphere for both the case of an overall perpendicular magnetic field and a homogeneous coaxial, thereby locally varying, magnetic field. For both magnetic -field configurations, we provide analytical solutions for spectra and eigenstates. For the experimentally relevant case of a coaxial magnetic field we find that the Landau levels split and one class shows a peculiar scaling proportional to B 1 / 4 , thereby characteristically differing from the usual linear B and B 1 / 2 dependence of the planar Schr & ouml;dinger and Dirac case, respectively. We compare our analytical findings to numerical results that we also extend to the case of the Minding surface.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | HYPERBOLIC PLANE; PATH-INTEGRATION; ELECTRONS; ANALOG; FORMS; FIELD; |
| Subjects: | 500 Science > 530 Physics |
| Divisions: | Physics > Institute of Theroretical Physics > Chair Professor Richter > Group Klaus Richter |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 07 Oct 2025 06:34 |
| Last Modified: | 07 Oct 2025 06:34 |
| URI: | https://pred.uni-regensburg.de/id/eprint/64253 |
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