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

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

1997-08-06

arxiv.org/abs/cond-mat/9708045v3

Phys. Rev. B 56, 12088-91 (1997)

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

9 pages, 3 figures, REVTEX, to appear in Phys. Rev. B, Sep. 15

Scientific paper

10.1103/PhysRevB.56.12088

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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