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Bloch Electrons in a Magnetic Field
Abstract
A formalism recently developed by the author is used to simplify Kohn's derivation of an effective Hamiltonian. The new derivation is valid for arbitrary symmetry and with the inclusion of spin-orbit effects and for bands with degeneracies. The actual form is obtained to second order in the magnetic field. It is explicitly shown that the procedure is asymptotically convergent. This Hamiltonian is then used to obtain the susceptibility in a convenient form. The nature of the actual energy levels is discussed with particular attention to the broadening, gaps in the continuous region, and magnetic breakdown.
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Citations
Cites
Quantum mechanics as a statistical theory
Moyal, J. E. (1949) · Mathematical Proceedings of the Cambridge Philosophical Society · doi:10.1017/s0305004100000487 · Cited by 3,116
Magnetic Breakdown in Crystals
Cohen, M. H., & Falicov, L. M. (1961) · Physical Review Letters · doi:10.1103/physrevlett.7.231 · Cited by 266
Cited by
Berry phase effects on electronic properties
Xiao, D., Chang, M.-C., & Niu, Q. (2010) · Reviews of Modern Physics · doi:10.1103/revmodphys.82.1959 · Cited by 5,277
Energy levels and wave functions of Bloch electrons in rational and irrational magnetic fields
Hofstadter, D. R. (1976) · Physical Review B · doi:10.1103/physrevb.14.2239 · Cited by 3,495
Colloquium : Artificial gauge potentials for neutral atoms
Dalibard, J., Gerbier, F., Juzeliūnas, G., & Öhberg, P. (2011) · Reviews of Modern Physics · doi:10.1103/revmodphys.83.1523 · Cited by 2,033
Experimental Realization of Strong Effective Magnetic Fields in an Optical Lattice
Aidelsburger, M., Atala, M., Nascimbène, S., Trotzky, S., Chen, Y.-A., & Bloch, I. (2011) · Physical Review Letters · doi:10.1103/physrevlett.107.255301 · Cited by 775
Nenciu, G. (1991) · Reviews of Modern Physics · doi:10.1103/revmodphys.63.91 · Cited by 374
Metadata
- Authors
- Blount, E. I.
- Venue
- Physical Review
- Publisher
- American Physical Society (APS)
- Published
- 1962-06-01
- Volume
- 126
- Issue
- 5
- Pages
- 1636-1653
- ISSN
- 0031-899X (ISSN-L)
- OpenAlex
- W2042471052
- Cited by
- 495
- References
- 2
- FWCI
- 9.94
- Type
- journal article
- Language
- en
- Open access
- closed
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Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
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