# Nature of superconducting fluctuation in photo-excited systems

## TL;DR

This paper investigates the behavior of superconducting fluctuations in photo-excited systems above the critical temperature using a time-dependent Ginzburg-Landau model, revealing exponential and power-law decay regimes influenced by relaxation rates.

## Contribution

It introduces a theoretical framework for understanding nonequilibrium superconducting fluctuations induced by photo-excitation, extending the critical region concept to excited states.

## Key findings

- Excited states decay exponentially at long times with a rate proportional to temperature difference from $T_c$.
- Intermediate times show power-law or logarithmic decay depending on excitation intensity.
- The critical region extends into the excited state, affecting the decay dynamics.

## Abstract

The photo-excited state associated with superconducting fluctuation above the superconducting critical temperature $T_c$ is studied based on the time-dependent Ginzburg-Laundau approach. The excited state is created by an electric-field pulse and is probed by a weak secondary external field, which is treated by the linear response theory mimicking pump-probe spectroscopy experiments. The behavior is basically controlled by two relaxation rates: one is $\gamma_1$ proportional to the temperature measured from the critical point $T - T_c$ and the other is $\gamma_2$ proportional to the excitation intensity of the pump pulse. The excited state approaches the equilibrium state exponentially in a long time $t \gg \gamma_1^{-1}$, while in the intermediate time domain we find a power-law or logarithmic decay with different exponents for $t\ll \gamma_2^{-1}$ and $\gamma_2^{-1} \ll t \ll \gamma_1^{-1}$, even though the system is located away from the critical point. This is interpreted as the critical point in equilibrium being extended to a finite region in the excited situation. The parameter dependences on both the pump and probe currents are also systematically studied in all dimensions.