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Energy spectrum for two-dimensional potentials in very high magnetic fields

Z. Gedik·M. Bayindir
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Abstract

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 delta 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.

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Z. Gedik, M. Bayindir. 1997-08-08. Energy spectrum for two-dimensional potentials in very high magnetic fields. https://doi.org/10.1103/physrevb.56.12088

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