Hofstadter's butterfly

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Hall conductance of Bloch electrons in a magnetic field D. Springsguth, R. Ketzmerick, and T. Geisel MPI fu¨r Stro¨mungsforschung und Institut fu¨r Nichtlineare Dynamik der Universita¨t Go¨ttingen, D-37073 Go¨ttingen, Germany ~Received 22 January 1997! We study the energy spectrum and the quantized Hall conductance of electrons in a two-dimensional periodic potential with perpendicular magnetic field without neglecting the coupling of the Landau bands. Remarkably, even for weak Landau band coupling significant changes in the Hall conductance compared to the one-band approximation of Hofstadter’s butterfly are found. The principal deviations are the rearrangement of subbands and unexpected subband contributions to the Hall conductance. @S0163-1829~97!07728-X