Phys. Rev. B 56, 12088–12091 (1997)Energy spectrum for two-dimensional potentials in very high magnetic fieldsReceived 10 March 1997; revised 29 May 1997; published in the issue dated 15 November 1997 A method, analogous to supersymmetry transformation in quantum mechanics, is developed for a particle in the lowest Landau level moving in an arbitrary potential. The method is applied to two-dimensional potentials formed by Dirac δ scattering centers. In the periodic case, the problem is solved exactly for rational values of the magnetic flux (in units of flux quantum) per unit cell. The spectrum is found to be self-similar, resembling the Hofstadter butterfly [Phys. Rev. B 14, 2239 (1976)]. © 1997 The American Physical Society URL:
http://link.aps.org/doi/10.1103/PhysRevB.56.12088
DOI:
10.1103/PhysRevB.56.12088
PACS:
71.70.Di, 73.20.Dx, 73.40.Hm
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