Electron-phonon coupling across the superconductor-insulator transition

We measured current-voltage characteristics on both sides of the magnetic-field-driven superconductor-insulator transition. On both sides, these show strong nonlinearities leading to a conduction branch that is independent of phonon temperature. We show that a picture of electron overheating can quantitatively explain our data over the entire magnetic field range. We find that electron-phonon coupling strength remains roughly constant throughout the insulating state and across the superconductor-insulator transition, dropping dramatically as the magnetic field approaches zero. Our findings shed light on the origin of the highly debated saturation of resistance at low temperature, which has been interpreted by some as evidence for a new anomalous metallic phase and by others as a result of electrons failing to cool down. At the heart of this treatment lies the assumption that resistance is a function of electron temperature and not the phononic one. The applicability of this framework implies that the conduction mechanism, present in the superconductor and throughout the insulating phase, does not rely on a phonon bath.

Figure 1

Comparison of $IV\text{"s}$ between the insulating state and the SC one. (a) $I$ vs $V$ of sample GCT22a at $B=7$ T, at which the sample is insulating. $I$ is presented in absolute value, on a log scale. (b) $V$ vs $I$ of sample AD12a, a lower-disorder sample that did not undergo a $B$-driven SIT, at $B=12$ T. $V$ is presented in absolute value, on a log scale. (c) $V$ vs $I$ of sample TL40a at $B=0.3$ T at which the sample is on the SC side of the $B$-driven SIT. $V$ is presented in absolute value on a log scale. In all plots the color scales correspond to the values of $T$ (see legends).

Figure 2

Heat-balance analysis. (a) $P$ vs inferred $T_{\mathrm{el}}$ of sample TL40a at $T=0.02$ K for a range of $B^{\prime }s$ (see legend) spanning both sides of the SIT ($B_c=$ 2.1 T). The data is presented in a log-log scale. (b) $P+\mathrm{\Gamma }\mathrm{\Omega }{T}_{\mathrm{ph}}^{\beta }$ vs inferred $T_{\mathrm{el}}$ of sample TL40a at $B=0.3$ T, at which the sample is in the SC state. The color scale corresponds to different $T\text{"s}$ (see legend). The data is presented in a log-log scale. Subfigures (a) and (b) share a common $x$ axis. (c) $I_{\mathrm{trap}}$ vs $B/B_c$ plotted on a log-lin scale on the bottom and left axes, and $V_{\mathrm{trap}}$ vs $B/B_c$ plotted on a log-lin scale on the bottom and right axes. Measured values are marked as circles and values acquired by graphical solution of the HB equation as squares.

Figure 3

Electron-phonon coupling strength and resulting saturation $T\text{"s}$. (a) $\beta$ vs $B$ plotted on a linear scale. The sample names and corresponding $B_c$'s are specified in the legend. The vertical dashed lines signify $B_c$ of each sample. (b) The same data plotted on a lin-log plot. The data from the insulator is omitted from this plot. The black lines are fits to the form $\beta ={\beta }_0-\alpha ln(B/B_c)$. (c) Expected saturation $T$ in the presence of external noise, treated as a constant $P_{\mathrm{ex}}={10}^{-12}$ W, plotted on a linear scale vs $B/B_c$ on a logarithmic scale. Subfigures (b) and (c) share a common $x$ axis.