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Bloch Electrons in Irrational Magnetic Fields by A. Rauh; G. H. Wannier; G. Obermair is a Physics and Astronomy article available to read on EtoBox.

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## Abstract A group‐theoretical analysis is given of the eigenstates of a charged particle when a magnetic field and a periodic potential are simultaneously present. The field is assumed totally or partially irrational with respect to the crystalline structure. The representations of the magnetic translation group are generated from free electron Landau states for convenience, but no discrepancies with the Frobenius method arise. The results are as follows: if **__H__** is parallel to a lattice direction, **__k · H__** is a good quantum number; otherwise, **__k · H__** may be assigned a fixed value for all members of a representation but is not numerically unique. According to group theory, there is a fixed finite δ__k__~⊥~ which separates members of the same representation, and hence, equal energy. However, consideration of the energy matrix shows that there is complete degeneracy in __k__~y~ for totally irrational fields; this case is thus close to the case of free electrons. In the cases intermediate between zero and totally irrational field boundary conditions may be crucial for the energy spectrum, as illustrated by an example.

Who reads Bloch Electrons in Irrational Magnetic Fields?

Author

A. Rauh; G. H. Wannier; G. Obermair

Publisher

John Wiley and Sons; Wiley (John Wiley & Sons); John Wiley & Sons Ltd.; Wiley (ISSN 0370-1972)

Published

1974

Language

EN

Field

Physics and Astronomy (Physical Sciences)