Transient Dynamics of $d$-Wave Superconductors after a Sudden Excitation

Motivated by recent ultrafast pump-probe experiments on high-temperature superconductors, we discuss the transient dynamics of a $d$-wave BCS model after a quantum quench of the interaction parameter. We find that the existence of gap nodes, with the associated nodal quasiparticles, introduces a decay channel which makes the dynamics much faster than in the conventional $s$-wave model. For every value of the quench parameter, the superconducting gap rapidly converges to a stationary value smaller than the one at equilibrium. Using a sudden approximation for the gap dynamics, we find an analytical expression for the reduction of spectral weight close to the nodes, which is in qualitative agreement with recent experiments.

Figure 1

Plot of the gap dynamics for the $d$-wave (full red line) and $s$-wave (dashed black line) symmetries and for different quench parameters ${\mathrm{\Delta }}_i/{\mathrm{\Delta }}_f$: (a) 0.001, (b) 0.2, (c) 4.0, and (d) 5.2. Inset of panel (b): log-log plot of the local maxima of the gap.

Figure 2

Plot of the stationary gap ${\mathrm{\Delta }}_{\text{st}}/{\mathrm{\Delta }}_f$ as a function of the quench parameter ${\mathrm{\Delta }}_i/{\mathrm{\Delta }}_f$ for the $d$-wave (full red line with full circles) and $s$-wave (dashed black line with empty circles) symmetries. For ${\mathrm{\Delta }}_i/{\mathrm{\Delta }}_f\lesssim 0.2$ the $s$-wave gap exhibits undamped oscillations around the value indicated with a square, in this case the circles indicate the extrema of the oscillations. Curves without symbols: equilibrium gap $\mathrm{\Delta }(T^{*})$ corresponding to an effective temperature $T^{*}$.