Real-space microscopic description of laser-pulse induced melting of superconductivity

Abstract

Quenching quantum order via laser pulses has proven a useful tool to access exotic physical effects in systems that are strongly perturbed out of equilibrium. However, theoretical modelling of experimental measurements is typically done phenomenologically or by assuming translational invariance due to the complexity of the problem. Here, we solve a microscopic real-space model of the time dynamics of a superconductor following an intense laser-pulse. We are able to reproduce recent experimental findings displaying a critical slowing-down of the melting of the order parameter for laser fluences close to the condensation energy. Moreover, we leverage the real-space resolution of our model to predict how phase fluctuations and currents in the system behave both spatially and temporally. We discover an unusual current flow in the superconductor after the pulse has subsided, resembling backward waves that normally require special engineering in metamaterials or wave guides. Our results predict a rich behavior of the superconducting order parameter at a microscopic level which is manifested in current textures that can be probed using radiation detection.

Figures (5)

• Figure 1: Melting time $\tau_m$ versus absorbed internal energy for different choices of inverse temperature $\beta = 1/T$. The black dots mark the melting time at the absorbed energy which equals the difference in internal energy of the superconducting and normal state at time zero, $\mathcal{E}_{\mathrm{sc}}$. The red dots mark the melting time at the absorbed energy where the average of the order parameter goes to zero at some point during the time evolution. Parameters used are $N_x = 100$ and $\omega = \gamma = 0$.
• Figure 2: Several time evolutions of the order parameter averaged over sites at inverse temperature $\beta = 35$ with different choices of the parameter $A_0$ varying between $1-3$. Parameters used are $N_x = 100$ and $\omega = \gamma = 0$.
• Figure 3: Direction and signed magnitude of currents of a slice of the superconductor at $\tau = 20$. The upper plot shows a slice $y_0 = 60$ for a superconductor without phonons. Both wavefronts are moving towards each other and the other end of the lattice as indicated by the red arrows, however the current is all in the $+x$-direction as indicated by the black arrrows. The lower plot shows a slice $x_0 = 60$ for a superconductor with phonons. Both wavefronts are moving towards each other but in this case the direction of the current is opposite that of the wavefront for both ends. Parameters used are $N_x = 120$, $A_0 = 2.2$, $\beta = 10000$ for both, and $\gamma = 0.05$, $\omega = 0.3$ for the case with phonons.
• Figure 4: Spatially resolved phase of the order parameters, $\mathrm{arg}(\Delta_i)$ at two different times, showing the correspondence between the gradient of the phase and the currents. Parameters used are $N_x = 120$, $A_0 = 2.2$, $\gamma = \omega = 0$ and $\beta = 10000$.
• Figure 5: Difference between $\langle | \Delta | \rangle$ and $|\langle \Delta \rangle |$, showing how coherence of phases between different lattice sites are lost after a reflection at the boundaries leading to a suppression of the order parameter. Parameters used are $N_x = 120$, $A_0 = 2.6$, $\gamma = \omega = 0$ and $\beta = 10000$.