Fourier analyses of commensurability oscillations in Fibonacci lateral superlattices

Abstract

Magnetotransport measurements have been performed on Fibonacci lateral superlattices---two-dimensional electron gases subjected to a weak potential modulation arranged in the Fibonacci sequence $LSLLSLS\dots{}$ with $L/S=\ensuremath{\tau}$ (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.