Quasiperiodic functions theory and the superlattice potentials for a two-dimensional electron gas

We consider Novikov problem of the classification of level curves of quasiperiodic functions on the plane and its connection with the conductivity of two-dimensional electron gas in the presence of both orthogonal magnetic field and the superlattice potentials of a special type. We show that the modulation techniques used in the recent papers on the two-dimensional (2-D) heterostructures permit us to obtain the general quasiperiodic potentials for 2-D electron gas and consider the asymptotic limit of conductivity when tau-->infinity. We use the quasiclassical approach introduced by Beenakker for the modulated electron gas and investigate the level curves of quasiperiodic potentials (Novikov problem) to get the asymptotic behavior of conductivity in this limit. Using the theory of quasiperiodic functions we introduce here the topological characteristics of the quasiperiodic potentials observable in the conductivity. The corresponding characteristics are the direct analog of the "topological numbers" introduced recently by Novikov and the present author in the conductivity of normal metals. (C) 2004 American Institute of Physics.