IThe energy spectrum of an electron in the presence of a uniform magnetic field and a potential of hexagonal symmetry is analyzed. Two alternative approaches are used, one that takes as a basis set freeelectron Landau functions, and a second one that treats an effective single-band Hamiltonian with the Peierls substitution. Both methods lead to consistent results. The energy spectrum is found to have recursive properties similar to those discussed by Hofstadter for the case of a square lattice. The density of states over each subband .of the spectrum has the same structure as that for the original field-free band. The plot of integrated density of states versus field is also discussed,
We investigate the delocalization and conductance quantization in finite one-dimensional chains with only off-diagonal disorder coupled to leads. It is shown that the appearance of delocalized states at the middle of the band under correlated disorder is strongly dependent upon the even-odd parity of the number of sites in the system. In samples with inversion symmetry the conductance equals 2e 2 /h for odd samples and is smaller for even parity. This result suggests that this even-odd behavior found previously in the presence of electron correlations may be unrelated to charging effects in the sample.
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