Abstract
An increasing current through a superconductor can result in a discontinuous increase in the differential resistance at the critical current. This critical current is typically associated either with breaking of Cooper-pairs or with the onset of collective motion of vortices. Here we measure the current–voltage characteristics of superconducting films at low temperatures and high magnetic fields. Using heat-balance considerations we demonstrate that the current–voltage characteristics are well explained by electron overheating enhanced by the thermal decoupling of the electrons from the host phonons. By solving the heat-balance equation we are able to accurately predict the critical currents in a variety of experimental conditions. The heat-balance approach is universal and applies to diverse situations from critical currents to climate change. One disadvantage of the universality of this approach is its insensitivity to the details of the system, which limits our ability to draw conclusions regarding the initial departure from equilibrium.
Highlights
An increasing current through a superconductor can result in a discontinuous increase in the differential resistance at the critical current
We present the results of a systematic study of Ic in superconducting a:InO at 0.5 > T > 0.01 K and B’s 12 ≥ B ≥ 9 T, for samples of various thicknesses in both perpendicular B (B⊥) and in-plane B (B∣∣)
∣I∣’s and a high resistive (HR) state at high ∣I∣’s. The transition between these states occurs discontinuously at two different Ic value; we define the measured I where the HR → LR transition occurs as IHc !L and the measured I where the LR → HR transition occurs as IcL!H
Summary
An increasing current through a superconductor can result in a discontinuous increase in the differential resistance at the critical current. The authors found that Ic ~ ∣B − Bc2∣α, with α ≈ 1.6 that is close to the mean-field value of 3/2 indicating, as they pointed out, that Ic is a result of the combined action of de-pairing and de-pinning where the increasing I initially suppresses the order parameter (by pairbreaking), helping the Lorentz force to overcome the pinning. While by using this approach they were able to suggest a resolution to the ubiquitous linear Bc2(T) as T → 010,11, their theory is not yet refined enough to offer a quantitative prediction to the value of Ic itself. To analyze this process we model our experiment as being comprised of four independent subsystems (Fig. 1a) that are thermally coupled via lumped thermal resistors (R~’s): The electrons, the host a:InO phonons, the substrate phonons and the liquid helium mixture (in which our sample is immersed in our dilution refrigerator)
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