Fourier analyses of commensurability oscillations in Fibonacci lateral superlattices

TL;DR

This study uses Fourier analysis to dissect the complex commensurability oscillations in Fibonacci lateral superlattices, revealing detailed information about the potential modulation affecting two-dimensional electron gases.

Contribution

It introduces a Fourier band-pass filtering method to isolate individual oscillation components, enabling reconstruction of the potential profile in Fibonacci superlattices.

Findings

Successful separation of oscillation components via Fourier filtering

Quantitative evaluation of potential modulation amplitudes

Reconstruction of the potential profile from magnetoresistance data

Abstract

Magnetotransport measurements have been performed on Fibonacci lateral superlattices (FLSLs) -- two-dimensional electron gases subjected to a weak potential modulation arranged in the Fibonacci sequence, LSLLSLS..., with L/S=tau (the golden ratio). Complicated commensurability oscillation (CO) is observed, which can be accounted for as a superposition of a series of COs each arising from a sinusoidal modulation representing the characteristic length scale of one of the self-similar generations in the Fibonacci sequence. Individual CO components can be separated out from the magnetoresistance trace by performing a numerical Fourier band-pass filter. From the analysis of the amplitude of a single-component CO thus extracted, the magnitude of the corresponding Fourier component in the potential modulation can be evaluated. By examining all the Fourier contents observed in the magnetoresistance trace, the profile of the modulated potential seen by the electrons can be reconstructed with some remaining ambiguity about the interrelation of the phase between different components.