Dynamics of the intermediate state in nonequilibrium superconductors

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Abstract
We report experimental measurements of the voltage response of current-biased superconducting thin films excited by 30-ps-FWHM (full width at half-maximum) pulsed laser radiation. Experiments performed with Pb and Sn films irradiated by a full train of laser pulses provide direct evidence for the existence of a nonstationary intermediate state. The state was observed during the superconducting-to-normal transition, as well as during the recovery of the film from the nonequilibrium normal state into the superconducting state. Single-pulse laser experiments enabled us to study the superconducting-to-normal transition in detail. Depending on the optical power, both triangular and quadruangular voltage pulses were observed. The triangular pulses had amplitudes dependent on the laser power and reflected the transition to the intermediate state, where superconducting and normal domains coexisted. The quadrangular pulses were associated with the full transition into the normal state. Very short triangular voltage pulses with full widths of the order of hundreds of picoseconds and rise times as short as about 100 ps were observed for thin Pb films illuminated by a low, near-threshold, laser power. The pulse rise time was almost constant and it only depended weakly on the film thickness, while the pulse width and the fall time were very sensitive to the optical input power as well as other experimental conditions (e.g., film thickness, Pb-substrate interface). The pulse decay was determined to be linear. The linear decay reflects a geometric relaxation of the intermediate state. An experiment performed with a stretched laser pulse (about 470 ps FWHM) demonstrated an initial thresholding effect and indicated that the subsequent voltage is proportional to the time integral of the laser pulse (optical energy). This confirms that the transition from the superconducting state to the normal state is a two-step transition. First, a sudden jump leads to the nonstationary, intermediate state followed by a gradual increase of the volume of the normal phase with a rate proportional to the rate of increase of the laser pulse energy. All of our observations are in good agreement with numerical simulations based on Elesin’s theory of the intermediate state.