Spectral analysis of universal conductance fluctuations

TL;DR

This paper analyzes the spectral properties of universal conductance fluctuations in thin wires, revealing a mostly discrete spectrum with a small continuous component, supporting a superposition of incommensurate harmonics scenario.

Contribution

It provides the first detailed Fourier analysis of experimental conductance fluctuation data, confirming the discrete harmonic structure and identifying a small continuous spectral component.

Findings

Spectrum is mostly discrete, consistent with incommensurate harmonics.

Existence of a small continuous spectral component is confirmed.

Results align with theoretical predictions and sample geometry estimates.

Abstract

Universal conductance fluctuations are usually observed in the form of aperiodic oscillations in the magnetoresistance of thin wires as a function of the magnetic field B. If such oscillations are completely random at scales exceeding \xi_B, their Fourier analysis should reveal a white noise spectrum at frequencies below \xi_B^{-1}. Comparison with the results for 1D systems suggests another scenario: according to it, such oscillations are due to the superposition of incommensurate harmonics and their spectrum should contain discrete frequencies. An accurate Fourier analysis of the classical experiment by Washburn and Webb reveals a practically discrete spectrum in agreement with the latter scenario. However, this spectrum is close in shape to the discrete white noise spectrum whose properties are similar to a continuous one. More detailed analysis reveals the existence of the continuous component, whose smallness is explained theoretically. A lot of qualitative results are obtained, which confirm the presented picture. The distribution of phases, frequency differences and the growth exponents agree with theoretical predictions. Discrete frequencies depends weakly on the treatment procedure. The discovered shift oscillations confirm the analogy with 1D systems. Microscopical estimates show agreement of the obtained results with geometrical dimensions of the sample.