Time-dependent universal conductance fluctuations in mesoscopic Au wires: Implications

In cold, mesoscopic conductors, two-level fluctuators lead to time-dependent universal conductance fluctuations (TDUCFs) manifested as $1∕f$ noise. In Au nanowires, we measure the magnetic-field dependence of TDUCFs, weak localization (WL), and magnetic-field-driven UCFs before and after treatments that alter magnetic scattering and passivate surface fluctuators. Inconsistencies between $L_{\varphi }^{\mathrm{WL}}$ and $L_{\varphi }^{\mathrm{TDUCF}}$ strongly suggest either that the theory of these mesoscopic phenomena in weakly disordered, highly pure Au is incomplete, or that the assumption that the TDUCF frequency dependence remains $1∕f$ to very high frequencies is incorrect. In the latter case, TDUCFs in excess of $1∕f$ expectations may have implications for decoherence in solid-state qubits.

Figure 1

The $2\mathrm{K}$ WL magnetoresistance of sample A before and after annealing. The size difference indicates a different coherence length before and after annealing. The solid lines are the theoretical fit to the data with $L_{\varphi }$ as the only fitting parameter.

Figure 2

The magnitude of the $1∕f$ TDUCF noise as a function of magnetic field for sample C at three different temperatures, normalized to its zero field value [see Eq. (2)]. The sample had been allowed to anneal at room temperature for one week when these data were taken. The solid lines are the theoretical fit to the data assuming unsaturated TDUCF, with $L_{\varphi }$ as the only fitting parameter.

Figure 3

Coherence lengths inferred from both WL magnetoresistance and TDUCF noise power vs magnetic field before annealing (top graph) and after $2\text{weeks}$ annealing (bottom graph). The sample has a Ti adhesion layer of $1.5\mathrm{nm}$. The solid line is the theoretical Nyquist dephasing length.

Figure 4

Normalized noise power vs $f$ before (open) and after (filled) sample annealing. The inset shows the noise power as a function of magnetic field before and after annealing. The larger upturn in the curve before annealing demonstrates a larger paramagnetic impurity concentration.

Figure 5

The normalized zero-field noise power before and after annealing with a $1.5\text{−}\mathrm{nm}$ Ti adhesion layer. The pre-anneal data is consistent with a saturated coherence length by $2\mathrm{K}$.

Figure 6

Coherence lengths inferred from WL and TDUCF noise power vs magnetic field before (top graph) and after (bottom graph) assembly of a dodecanethiol SAM. The solid line is the theoretical Nyquist dephasing time. Solid squares are from weak localization measurements. Open circles assume unsaturated TDUCF, while open triangles assume saturated TDUCF.

Figure 7

The normalized noise power of sample B before and after assembly of a dodecanethiol SAM. The sample has no Ti adhesion layer.

Figure 8

Filled shapes represent the ratios of the unsaturated $L_{\varphi }^{\mathrm{TDUCF}}$ to $L_{\varphi }^{\mathrm{WL}}$ both pre- and post-SAM assembly. The precision of the data coupled with the large error bars indicate that the unsaturated crossover function is not the correct functional form. The open shapes show the noise power ratios of pre- and post-SAM to pre-SAM assembly.

Figure 9

The $2\mathrm{K}$ magnetofingerprint of sample B before and after SAM assembly. Only one sweep is shown for each curve. The curves have been offset for clarity.