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Ground state of a spin-½ charged particle in a two-dimensional magnetic field
Abstract
We prove that a spin-\textonehalf{} charged particle moving in a plane under the influence of a perpendicular magnetic field has ($N\ensuremath{-}1$) zero-energy states, where $N$ is the closest integer to the total flux in units of the flux quantum. The ($N\ensuremath{-}1$) independent wave functions are calculated explicitly. The result, which is extremely simple to prove, is an example of the Atiyah-Singer index theorem when applied to the Euclidean two-dimensional Dirac equation.
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Citations
Cited by
Evers, F., & Mirlin, A. D. (2008) · Reviews of Modern Physics · doi:10.1103/revmodphys.80.1355 · Cited by 2,092
Fukushima, K., Kharzeev, D. E., & Warringa, H. J. (2008) · Physical Review D · doi:10.1103/physrevd.78.074033 · Cited by 2,006
Edge Modes, Degeneracies, and Topological Numbers in Non-Hermitian Systems
Leykam, D., Bliokh, K. Y., Huang, C., Chong, Y. D., & Nori, F. (2017) · Physical Review Letters · doi:10.1103/physrevlett.118.040401 · Cited by 772
Integer quantum Hall transition: An alternative approach and exact results
Ludwig, A. W. W., Fisher, M. P. A., Shankar, R., & Grinstein, G. (1994) · Physical Review B · doi:10.1103/physrevb.50.7526 · Cited by 709
Kharzeev, D. E., & Warringa, H. J. (2009) · Physical Review D · doi:10.1103/physrevd.80.034028 · Cited by 324
Metadata
- Authors
- Aharonov, Y., & Casher, A.
- Venue
- Physical Review A
- Publisher
- American Physical Society (APS)
- Published
- 1979-06-01
- Volume
- 19
- Issue
- 6
- Pages
- 2461-2462
- ISSN
- 0556-2791 (ISSN-L)
- OpenAlex
- W2080702897
- Cited by
- 449
- References
- 0
- FWCI
- 0.45
- Type
- journal article
- Language
- en
- Open access
- closed
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- Aharonov, Y., & Casher, A. (1979). Ground state of a spin-½ charged particle in a two-dimensional magnetic field. Physical Review A. https://doi.org/10.1103/physreva.19.2461
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