Nonequilibrium hysteretic phase transitions in periodically light-driven superconductors

Abstract

We find nonequilibrium phase transitions accompanied by multiple (nested) hysteresis behaviors in superconductors coupled to baths under a time-periodic light driving. The transitions are demonstrated with a full phase diagram in the domain of the driving amplitude and frequency by means of the Floquet many-body theory. In the weak driving regime with a frequency smaller than half of the superconducting gap, excited quasiparticles are accumulated at the far edges of the bands, realizing a distribution reminiscent of the Eliashberg effect, which suddenly becomes unstable in the strong driving regime due to multi-photon-assisted tunneling across the gap mediated by the in-gap Floquet sidebands. We also show that superconductivity is enhanced in the weak driving regime without effective cooling, which is attributed to the modulation of the spectrum due to Floquet sidebands.

Figures (3)

• Figure 1: (a) Schematic picture of quasiparticles (holes) in superconductors driven by light shown by filled (empty) circles. Intraband scattering leads to an effective cooling of the system (Eliashberg effect), while there can occur multi-photon-assisted tunneling across the gap through Floquet sidebands (small peaks inside the gap). (b) Phase diagram of a BCS superconductor coupled to baths under a time-periodic light driving in the domain of the driving amplitude $A$ and frequency $\Omega$. The color code plots the time-averaged superconducting order parameter $\Delta_0$ rescaled by the equilibrium one $\Delta_{\rm eq}$. The area surrounded by the orange (green) curve indicates the (nested) hysteresis regime. The phase diagram is computed with $U=6.0$, $\Gamma=0.1$, and $T=0.2$, which gives $\Delta_{\rm eq}\approx 2.4$.
• Figure 2: Relative changes of (a) the superconducting order parameter $\delta\Delta/\Delta_{\rm eq}(\approx 2.4)$ and (b) the effective temperature $\delta T/T$ as a function of the driving amplitude $A$. (c) Changes of the effective distribution $\delta f(\omega)$. The inset shows an enlarged view of $\delta f(\omega)$. The gray solid line shows the time-averaged spectral function $A_0(\omega)$ for $A=0$, whose maximum is normalized to 0.4. (d) Changes of the spectral function $\delta A_0(\omega)$, which has been normalized to set the maximum of $A_0(\omega)$ at $A=0$ to $1.0$. (e) Momentum-dependent spectral function $A_0(\boldsymbol k,\omega)$ for $\Omega=1.0$ and $A=0.6$. The number $n$ marks the Floquet sidebands. The inset shows the path in the Brillouin zone. The other parameters are $U=6.0$, $\Gamma=0.1$, and $T=0.2$.
• Figure 3: (a) Hysteresis behavior of $\Delta_0$ as a function of $A$ with different driving frequencies. The upper (lower) branches correspond to $\Delta_0$ computed from those with smaller (larger) $A$. The horizontal dashed lines indicate $\Delta_0=\Omega$. The red arrows show sudden jumps of $\Delta_0$ for $\Omega=1.0$. (b) Enlarged view of $\Delta_0$ in the region marked by the gray dashed curve in (a). The black curves with triangle markers show the nested hysteresis behavior of $\Delta_0$ for $\Omega=1.0$. The black dashed horizontal line shows $\Delta_0=2\Omega=2.0$. (c) Effective distributions for $\Omega=1.0$ and $A=1.2$ corresponding to the upper (dark red) and lower (orange) branches of the hysteresis loop. The blue curve is the Fermi-Dirac distribution with $T=0.2$ for reference. The other parameters are $U=6.0$, $\Gamma=0.1$, and $T=0.2$, which gives $\Delta_{\rm eq}\approx 2.4$.