Phase slips in a current-biased narrow superconducting strip

The theory of current transport in a narrow superconducting strip is revisited taking the effect of thermal fluctuations into account. The value of voltage drop across the sample is found as a function of temperature (close to the transition temperature, $T-T_{\mathrm{c}}$ $\ll T_{\mathrm{c}}$) and bias current $J<J_{\mathrm{c}}$ ($J_{\mathrm{c}}$ is the critical current calculated in the framework of the BCS approximation, neglecting thermal fluctuations). It is shown that careful analysis of vortices crossing the strip results in considerable increase of the activation energy.

Figure 1

Distribution of the current flowing in the strip in the presence of a vortex located in distance $r_1$ from the edge of the strip.

Figure 2

Distribution of the modulus of the order parameter in the strip with flowing current disturbed in the presence of a vortex: (a) transversal distribution at $y=0$ and (b) longitudinal distribution at $x=0$.

Figure 3

Positions of the zeros of the saddle-point solutions with one (a), two (b), etc., vortices. Here by means of $\{+,-\}$ are denoted the vorticities (phase factor changes by $\pm 2\pi$ for anticlockwise or clockwise circulation of the order-parameter zeros).

Figure 4

Excess activation energy related to the account for the true mechanism of the vortices penetration in the strip as the function of flowing current.