Observation of disorder-induced weakening of electron-phonon interaction in thin noble-metal films

We have used symmetric normal metal-insulator-superconductor (NIS) tunnel junction pairs, known as SINIS structures, for ultrasensitive thermometry in the temperature range $50–700\mathrm{mK}$. By Joule heating the electron gas and measuring the electron temperature, we show that the electron-phonon $\left(e\text{−}p\right)$ scattering rate in the simplest noble-metal disordered thin films (Cu,Au) follows a $T^4$ temperature dependence, leading to a stronger decoupling of the electron gas from the lattice at the lowest temperatures. This power law is indicative $e\text{−}p$ coupling mediated by vibrating disorder, in contrast to the previously observed $T^3$ and $T^2$ laws.

Figure 1

(a) A SEM image of a sample. The horizontal lines are Cu wires, the vertical lines are Al leads that form the junctions at the intersections with the Cu line. The insets are enlargements of the areas where the junctions are located. Note that the pure Al vertical lines (black) make contact with the horizontal Cu lines, the lighter gray vertical lines consist of $\mathrm{Al}+\text{shadows}$ from the Cu evaporation. (b) A schematic of the sample and the measurement circuit. SINIS bias circuit is fully floating with respect to the heating circuit, thus no heating current flows through the NIS junctions at dc.

Figure 2

(Color online) Calibration data for a typical SINIS thermometer biased at $I=60\mathrm{pA}$. Black line is the experimental data, and red dots the BCS-theory result. For the BCS-theory points, $\Delta$ and $R_T$ were determined independently from the experimental $I\text{−}V$ characteristics. From this data we estimate the temperature sensitivity $\delta T=(dT∕dV)\delta V\approx 0.1\mathrm{mK}$ rms, where $\delta V$ is the rms noise voltage. Inset, measured responsivity $dV∕dP$ of a SINIS vs the bias current.

Figure 3

(Color online) The electron temperature of (a) $t=33\mathrm{nm}$ Cu wire (blue) and $t=57\mathrm{nm}$ Au wire (red) vs applied Joule heating power in log-log scale. (b) Same for $t=84\mathrm{nm}$ (blue) and $t=140\mathrm{nm}$ (red) Cu wires. Dashed black lines are fits of the form $T={(P∕A)}^{1∕6}$, corresponding to the disordered $e\text{−}p$ scattering theory [Eq. (1)]. Dashed gray line is a fit $T={(P∕A)}^{1∕5}$. $T_{\text{bath}}=60\mathrm{mK}$.

Figure 4

(Color online) The logarithmic numerical derivative $d\left(\log T_e\right)∕d\left(\log P\right)$ of the same data as in Fig. 3 (points). (a) Cu $t=33\mathrm{nm}$, (b) Au $t=57\mathrm{nm}$, (c) Cu $t=84\mathrm{nm}$, and (d) Cu $t=140\mathrm{nm}$. Blue line equals $1∕5$, red $1∕6$, and green $1∕7$.