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

TL;DR

This paper explores the mathematical classification of quasiperiodic functions and their impact on the conductivity of a two-dimensional electron gas influenced by superlattice potentials and magnetic fields, introducing topological invariants.

Contribution

It connects the Novikov problem of quasiperiodic level curves with the physical conductivity in 2D electron gases, proposing topological characteristics as observable invariants.

Findings

General quasiperiodic potentials can be realized in 2D electron gases.

Topological characteristics of these potentials influence conductivity.

Asymptotic conductivity behavior analyzed as $ au ightarrow abla$ infinity.

Abstract

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 special type. We show that the modulation techniques used in the recent papers on the 2D heterostructures permit to obtain general quasiperiodic potentials for 2D electron gas and consider the asymptotic limit of conductivity when $\tau \rightarrow \infty$. Using the theory of quasiperiodic functions we introduce here the topological characteristics of such potentials observable in the conductivity. The corresponding characteristics are the direct analog of the "topological numbers" introduced previously in the conductivity of normal metals.