Time-dependent universal conductance fluctuations and coherence in AuPd and Ag

Quantum transport phenomena allow experimental assessment of the phase coherence information in metals. We report quantitative comparisons of coherence lengths inferred from weak localization magnetoresistance measurements and time-dependent universal conductance fluctuation data. We describe these two measurements and their analysis. Strong agreement is observed in both quasi-two-dimensional and quasi-one-dimensional (1D) AuPd samples, a metal known to have high spin-orbit scattering. However, quantitative disagreement is seen in quasi-1D Ag wires below $10\mathrm{K}$, a material with intermediate spin-orbit scattering. We consider explanations of this discrepancy, with particular emphasis on the theoretical expressions used to analyze the field dependence of the conductance fluctuations. We also discuss the mechanism of the suppression of conductance fluctuations at high drive levels, and dephasing mechanisms at work in these systems.

Figure 1

“Magnetofingerprint” measurements on sample I made using the five terminal bridge technique. The curves from top to bottom are at 2, 8, and $14\mathrm{K}$. The curves are offset for clarity.

Figure 2

WL magnetoresistance curves at various temperatures for a 43 and $500\mathrm{nm}$ AuPd wire (samples A and C) and a $140\mathrm{nm}$ Ag wire (sample F). Quasi-1D data shifted to pass through origin.

Figure 3

Noise power data from Ag sample F at 2, 14, and $20\mathrm{K}$. The crossover field becomes larger as the coherence length diminishes. The $20\mathrm{K}$ data do not drop by a full factor of 2 due to local interference noise.

Figure 4

(a) Coherence lengths as a function of $T$ for the AuPd samples (lettered accordingly). Triangle points are inferred from Eq. (4), circles are inferred from Eq. (6), and squares are inferred from WL. Only one UCF fit is shown in quasi-2D since the two results only differ by 3%. The dashed lines show the predicted dephasing length due to Nyquist scattering calculated from sample parameters. The solid line represents the calculated thermal length. (b) Coherence lengths as a function of $T$ for Ag samples E and F (lettered accordingly). Circle points are inferred from Eq. (8), and squares are inferred from WL. The dashed lines show the predicted dephasing length due to Nyquist scattering calculated from sample parameters. The solid line represents the calculated thermal length. Unlike the AuPd case, there is a statistically significant discrepancy between $L_{\varphi }^{\mathrm{WL}}$ and $L_{\varphi }^{\mathrm{TDUCF}}$ in these samples.

Figure 5

Coherence lengths from sample F. Squares are from WL, circles are inferred via the unsaturated TDUCF crossover function, and triangles are calculated with the saturated TDUCF crossover function.

Figure 6

Sensitivity of the noise power of sample E to applied current. Enhanced suppression of the noise occurs when $e{V}_{\mathrm{c}}$ becomes larger than the correlation energy. The drop-off current at $8\mathrm{K}$, $2\mathrm{T}$ is the same as $8\mathrm{K}$, $0\mathrm{T}$ implying that the coherence length is not sensitive to large applied fields.

Figure 7

(Color online) Normalized noise power of sample J at $2\mathrm{K}$ as a function of field for three different values of drive current (rms $500\mathrm{nA}$, $1\mu \mathrm{A}$, and $2\mu \mathrm{A}$). The unchanging crossover field demonstrates explicitly that the inferred $L_{\varphi }^{\mathrm{TDUCF}}$ is not affected strongly by drive level. Left inset: dimensionless conductance noise power as a function of drive current at zero field, showing that the higher drive currents do suppress the magnitude of the TDUCF. Right inset: log-log plot of the normalized noise power as a function of frequency at $2\mathrm{K}$, $2\mu \mathrm{A}$ drive, for three different values of $B$, showing the $1∕f$ dependence typical for all the TDUCF data in this work.

Figure 8

(Color online) (a) High field noise data for samples C, D, and F, all at $2\mathrm{K}$. The upturn at high fields implies that non-negligible concentrations of magnetic impurities exist in the AuPd samples. (b) High field noise data for sample B at several temperatures, showing the upturn in this nominally clean AuPd sample. The lines connecting the points for each temperature are a guide to the eye. Note that the upturn is smaller and happens at higher fields for higher temperatures, consistent with Zeeman splitting of magnetic impurities.