Inverse flux quantum periodicity of magnetoresistance oscillations in two-dimensional short-period surface superlattices

TL;DR

This paper analyzes magnetoresistance oscillations in a 2D electron gas with short-period surface superlattices, revealing inverse flux quantum periodicity and explaining experimental observations through theoretical modeling.

Contribution

It introduces a theoretical framework showing inverse flux quantum periodicity in magnetoresistance oscillations for short-period superlattices, aligning with recent experimental findings.

Findings

Prominent peaks in magnetoresistivity occur when one flux quantum passes through an integer number of unit cells.

Oscillation phases depend on the modulation periods involved.

Short-period superlattices exhibit distinct oscillation features compared to longer periods.

Abstract

Transport properties of the two-dimensional electron gas (2DEG) are considered in the presence of a perpendicular magnetic field $B$ and of a {\it weak} two-dimensional (2D) periodic potential modulation in the 2DEG plane. The symmetry of the latter is rectangular or hexagonal. The well-known solution of the corresponding tight-binding equation shows that each Landau level splits into several subbands when a rational number of flux quanta $h/e$ pierces the unit cell and that the corresponding gaps are exponentially small. Assuming the latter are closed due to disorder gives analytical wave functions and simplifies considerably the evaluation of the magnetoresistivity tensor $\rho_{\mu\nu}$. The relative phase of the oscillations in $\rho_{xx}$ and $\rho_{yy}$ depends on the modulation periods involved. For a 2D modulation with a {\bf short} period $\leq 100$ nm, in addition to the Weiss oscillations the collisional contribution to the conductivity and consequently the tensor $\rho_{\mu\nu}$ show {\it prominent peaks when one flux quantum $h/e$ passes through an integral number of unit cells} in good agreement with recent experiments. For periods $300- 400$ nm long used in early experiments, these peaks occur at fields 10-25 times smaller than those of the Weiss oscillations and are not resolved.