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Wannier functions for lattices in a magnetic field: II. Extension to irrational fields

Wilkinson, Michael (2000) Wannier functions for lattices in a magnetic field: II. Extension to irrational fields. Journal of Physics: Condensed Matter, 12 (23). pp. 4993-5009. ISSN 0953-8984

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Abstract

This paper extends earlier work on the definition of Wannier functions for Bloch electrons in a magnetic field. Extensions to irrational as well as rational magnetic fields are defined, and their properties investigated. The results are used to give a generalization of the Peierls effective Hamiltonian which is valid when the magnetic flux per unit cell is close to any rational number.