1998/09/07 by Uwe Grimm, Florian Gagel, Michael Schreiber
Physics and Astronomy · #cond-mat.mes-hall
published as Proceedings of the 6th International Conference on Quasicrystals, Eds. S. Takeuchi and T. Fujiwara (World Scientific, Singapore, 1998), pp. 188-191 · 4 pages, 5 PostScript figures, uses sprocl.sty (included)
arxiv created 1998/09/07 · arxiv updated 2009/11/30
The dc conductance and the Hall voltage of planar arrays of interconnected quantum wires are calculated numerically. Our systems are derived from finite patches of aperiodic graphs, with completely symmetric scatterers placed on their vertices which are interconnected by ideal quantum wires. Already in a periodic square lattice arrangement, quantum interference effects lead to complicated magnetotransport properties related to the Hofstadter butterfly. For rectangular Fibonacci grids and other quasiperiodic lattices, we obtain still more complex fractal patterns. In particular, irrational ratios of edge lengths and of tile areas in our samples destroy the periodicities with respect to the Fermi wave vector and the magnetic flux, respectively.