Enhancement and decrease of critical current due to suppression of superconductivity by a magnetic field

We present experimental results on the transport properties of a superconducting aluminum loop connected to reservoirs. As function of the applied magnetic field, an unexpected behavior is found—a steep enhancement (for temperatures close to the critical temperature) and a sharp drop (at lower temperatures) of the critical current at some value of the magnetic field $B_a^{*}\left(T\right)$. These effects are a consequence of a sudden suppression of superconductivity at $B_a=B_a^{*}$ in the banks to which the loop is attached by the current leads. As a result, the normal metal–superconductor boundaries appear at the ends of the current leads and the quasiparticle distribution function $f\left(E\right)$ in the superconductor deviates strongly from its equilibrium value. Calculations based on the Usadel equations show that the critical current should be enhanced at high temperature (due to the penetration of the normal current from the normal metal–superconductor boundaries), whereas at low temperatures, the suppression of the order parameter by the nonequilibrium $f\left(E\right)$ dominates and the critical current decreases. The latter provides a direct experimental verification of the recently proposed mechanism of the destruction of superconductivity by an applied voltage [R. S. Keizer, M. G. Flokstra, J. Aarts, and T. M. Klapwijk, Phys. Rev. Lett. 96, 147002 (2006)].

Figure 1

A scanning electron microscope image of the aluminum loop with attached current and voltage electrodes.

Figure 2

(Color online) Current-voltage characteristics of the superconducting loop at different values of the magnetic field and $T=0.982T_c$. The dotted curve corresponds to the normal state of our system. At current $I_c^{-}$, the loop transits from the normal to the superconducting state, and at $I=I_c^{+}$, from the superconducting to the normal state.

Figure 3

(Color online) Contour plot of the voltage drop $V$ at the loop as a function of the applied dc $I_a$ and the magnetic field $B_a$ measured at (a) $T=0.982T_c$ and (b) $T=0.962T_c$.

Figure 4

(Color online) Current-voltage characteristics of our model system at different temperatures, obtained in the voltage-driven regime $(B_a=0)$. The curves stop at the points where our model system transits to the normal state. Arrows on two of the curves indicate the values of the negative $\mid I_c^{-}\mid$ and positive $I_c^{+}$ critical currents measured in our experiment. The current is normalized to the Ginzburg-Landau depairing current $I_{GL}\left(T\right)$.

Figure 5

(Color online) Distribution of the order parameter (solid symbols) and the electrostatic potential (open symbols) along our model system (at $T=0.98T_c$) for two voltages which roughly correspond to $I\simeq I_c^{+}$ and $I\simeq I_c^{-}$. In both cases, the superconducting voltage leads near the loop will measure zero voltage although there is a voltage drop near the loop.

Figure 6

(Color online) Distribution of the (a) potential ${\Psi }_1$, normal current, and (b) order parameter along our system for relatively low $(T=0.92T_c)$ and high $(T=0.99T_c)$ temperatures.

Figure 7

(Color online) Current-voltage characteristics of our model system at zero and half magnetic flux quantum through the loop. At high temperature, both currents $I_c^{\pm }$ vary with magnetic field, while at low temperature, only the current $I_c^{-}$ changes.

Figure 8

(Color online) Current-voltage characteristics of our model system at different magnetic fields at $T=0.95T_c$. There is a gradual decrease of the hysteresis in the current-driven regime with increasing magnetic field (compare with Fig. 4). Dashed lines mark the voltage interval where there is no stationary superconducting state in the current leads.