Conductance switching and nonequilibrium phase coexistence in superconductors with intermediate bias

TL;DR

The study probes current–voltage relations in a 3D Nb superconducting film under intermediate bias, enabling finite voltages to develop across the sample and revealing nonequilibrium steady states not accessible under current bias. A sharp negative differential conductance appears at the S→N transition, consistent with the principle of minimum entropy production for the critical current event. The experiment shows phase coexistence in which superconducting and normal fractions intermingle without applied magnetic field, evidenced by fractional $\eta$ values in the relation $R_s = \eta R_n$ with $\eta \in [0,1]$. The results reveal bistability and distinct regimes between low-$r_L$ voltage bias and high-$r_L$ current bias, with a characteristic current $I_d$ given by $I_d = I_c/(1 + R_n / r_L)$ and retrapping current $I_r$ delimiting the hysteresis. Overall, the work demonstrates how controlling boundary conditions via intermediate biasing can engineer novel nonequilibrium states in macroscopic superconductors, with implications for superconducting electronics and the dissipative organization of states.

Abstract

Superconducting systems may display different types of nonequilibrium states depending on the specific constraints imposed for measurement. We probe current-voltage relations of three-dimensional superconducting films by allowing finite voltages to develop across their length. Our experiments reveal sharp features of negative differential conductance which highlight the validity of the principle of minimum entropy production at the critical current transition. We have observed dissipative states with resistances intermediate between those of superconducting and normal phases at zero applied magnetic field, indicating a phenomenon of phase coexistence under nonequilibrium conditions. The features of steady states reported here are not accessible in conventional transport experiments with current-biasing methods.

Figures (2)

• Figure 1: (a) Circuit for the measurement of current-voltage relations. (b) Expected plot of current ($I$) in the circuit as a function of applied voltage $V$. (c) Circuit used for electrical measurements on a superconducting film in Hall bar geometry. (d) Measurement of resistance ($R$) as a function of temperature ($T$) in four-probe configuration showing the superconducting transition. (e)$I$-$V$ curve measured for the circuit outlined in (c) for the superconductor-to-normal transition at $T$ = 6.85 K. (f)$I$-$V$ curves measured for both directions of voltage sweep at three different temperatures. (g,h) Voltage drop ($v_s$) across the superconductor ploted as a function of current ($I$) for two different values of resistance $r_L$ at $T$ = 6.85 K. (i) Plot of the parameter $\eta$ as a function of $v_s$ for the normal-to-superconductor transition.
• Figure 2: (a) Voltage drop ($v_s$) across the superconductor plotted as a function of current ($I$) at $T$ = 7.00 K. This shows the superconductor-to-normal transition for two different measurements using different values of $r_L$. The states within the dashed ellipse correspond to the nonequilibrium phase coexistence phenomenon. (b) Plot of the parameter $\eta$ as a function of $v_s$ for the superconductor-to-normal transition.