Self-similarity and novel sample-length-dependence of conductance in quasiperiodic lateral magnetic superlattices

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We study the transport of electrons in a Fibonacci magnetic superlattice produced on a two-dimensional electron gas modulated by parallel magnetic field stripes arranged in a Fibonacci sequence. Both the transmission coefficient and conductance exhibit self-similarity and the six-circle property. The presence of extended states yields a finite conductivity at infinite length, that may be detected as an abrupt change in the conductance as the Fermi energy is varied, much as a metal-insulator transition. This is a unique feature of transport in this new kind of structure, arising from its inherent two-dimensional nature.