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77, 131 (1996); M. Potthoﬀ, T. Wegner and V. Nolting, Phys. Rev. B 55, 16132 (1997). I. I. Katsnelson, Phys. Rev. B 57, 6884 (1998). [9] R. Lopez et al. Phys. Rev. Lett. 81, 4688 (1998). [10] A. Levy Yeyati, F. Flores and A. Mart´ın-Rodero, Phys. Rev. Lett. 83, 600 (1999). [11] B. Bell and A. Madhukar, Phys. rev. B 14, 4281 (1976). [12] J. Hubbard, Proc. Roy. Soc. A 276, 238 (1963). M. C. Ward, Phys. Rev. 118, 1417 (1960). C. Langreth, Phys. Rev. 150, 516 (1966). [15] Y. S. Wingreen, Phys. Rev.

Therefore, the eigenfunctions are of the form φ(x) = eiθx x uθx (x) with uθx (x + 2π) = uθx (x) and U can be represented as an inﬁnite matrix depending on the Bloch phase θx . This phase corresponds to the phase ν in the Harper Hamiltonian (1) and will be ﬁxed to be zero in the following. We have stated already in section 1 that for K, L → 0 with K/L = const. the spectrum of the KHM is given by the Harper spectrum. Concerning the properties (i)-(iii) it is already clear from the analysis in the preceding section that they could all be due to avoided band crossings.

12] J. Hubbard, Proc. Roy. Soc. A 276, 238 (1963). M. C. Ward, Phys. Rev. 118, 1417 (1960). C. Langreth, Phys. Rev. 150, 516 (1966). [15] Y. S. Wingreen, Phys. Rev. Lett. 68, 2512 (1992). [16] J. Schmid, J. Weis, K. Ederl and K. v. Klitzing, Physica B 256-258, 182 (1998). H. W. Holleitner1 , H. Qin1 , F. V. Ustinov2 , K. P. Kotthaus1 1 2 3 Center for NanoScience and Sektion Physik, Ludwig-Maximilians-Universit¨ at, Geschwister-Scholl-Platz 1, 80539 M¨ unchen, Germany. Physikalisches Institut III, Universit¨ at Erlangen-N¨ urnberg, Erwin-Rommel-Str.