Giant Resonant Enhancement of Photoinduced Dynamical Cooper Pairing, far above $T_c$

TL;DR

The paper addresses giant resonant enhancement of light-induced superconductivity in $\mathrm{K}_3\mathrm{C}_{60}$ (K3C60), observed up to room temperature near $50\,\text{meV}$, and not tied to a single IR phonon. It introduces a minimal time-dependent non-linear Holstein model where parametric driving of Raman Hg phonons creates a time-dependent electron–phonon coupling, which via a dissipative Schrieffer–Wolff transformation yields an effective $U(t)$ with a resonant AC component. A Floquet–BCS analysis shows that the resonant modulation of the AC part $U_1$—amplified by the Floquet factor $\mathcal{R}(\omega_{\rm dr})$ near resonance—drives instabilities at $T_c^*$ well above the equilibrium $T_c$, with $T_c^*/T_c$ can exceed $20$ for suitable parameters (e.g., $\mathcal{Q}=\omega/\gamma$). The model qualitatively reproduces the broad photo-susceptibility resonances that cluster around the Raman Hg modes and provides experimentally testable predictions such as coherent phonon oscillations and modest temperature dependence of line shapes. Overall, it offers a general mechanism for photoinduced superconductivity in driven electron–phonon systems and a framework to interpret and guide time-resolved experiments on K3C60 and related materials.

Abstract

Pump-probe experiments performed on $\mathrm{K}_3\mathrm{C}_{60}$ have unveiled both optical and transport signatures of metastable light-induced superconductivity up to room temperature, far above $T_c$. Recent experiments have uncovered that excitation in the vicinity of $50 ~\textrm{meV}$ enables the observation of high temperature light-induced superconductivity at significantly lower fluences. Inspired by these experiments we develop a mechanism which can explain such a giant resonant enhancement of light-induced superconductivity. Within a minimal non-linear Holstein model, we show that resonantly driving optical Raman modes leads to a time-dependent electron-phonon coupling. Such a coupling then modulates the effective electron-electron attraction, with the strongest modulations occurring when the drive is resonant with the phonon frequency. These dynamical modulations of the pairing interactions lead to Floquet-BCS instabilities at temperatures far exceeding equilibrium $T_c$, as observed in experiments. We conclude by discussing the implications of our general analysis on the $\mathrm{K}_3\mathrm{C}_{60}$ experiments specifically and suggesting experimental signatures of our mechanism.

Figures (3)

• Figure 1: High-$T_c^\star$ Dynamical Cooper Pairing in the Time-Dependent Holstein Model. (a) $T_c^\star/T_c$---obtained by solving Eq. \ref{['eq:floquet_bcs_equation']} within the the time-dependent Holstein model (Eq. \ref{['eq:time_dependent_holstein']}) with $A_0 = 0.2$---for two different $\mathcal{Q} = \frac{\omega}{\gamma}$ factor phonon modes. Dashed gray lines refer to analytic asymptotics at low (see text) and high frequencies (convergence to $T_c$). (b) The static contribution to the interaction $U_0/U_{\rm eq}$---where $U_{\rm eq} = U_{\rm bi}$---showing (small) resonant enhancement (suppression) under red-detuned (blue-detuned) driving. (c) The AC contribution to the interaction at the drive frequency $U_1/U_{\rm eq}$ showcasing giant, unsigned enhancement in the vicinity of resonant driving. This resonant contribution drives the resonant enhancement of $T_c^\star$. (d) A comparison---for $\mathcal{Q} = 10$---between $T_c^\star$ from a full Floquet calculation (teal) and $T_c(U_0)$ obtained within BCS theory (black), underscoring the Floquet nature of the BCS instability.
• Figure 2: Giant Resonant Enhancement of Photoinduced Cooper Pairing via Parametric Driving (a) $T_c^\star/T_c$ shown as a function of frequency $\omega_{\rm dr}/\omega$ and the energy scale associated with the electric field $\beta E_0^2/M$. Black lines reveal contours ($1\times, 10 \times, 30 \times$ enhancement); the purple line demarcates the parametrically unstable region; orange, green, blue are the cuts used to generate (b); yellow, green, pink dashed lines are the cuts used to generate (c). (b) $T_c^\star/T_c$ at fixed $\omega_{\rm dr}/\omega$ as a function of the electric field. (c) $T_c^\star/T_c$ at fixed $E_0$, as a function of normalized drive frequency.
• Figure 3: Photo-susceptibility. (a) Photo-susceptibility of light-induced superconductivity for the model given by Eq. \ref{['eq:BasicModelFull']} for two different temperatures $T = 2T_c$ (blue) and $T=20 T_c$ (red). (b) Schematic of the phononic density of states $F(\omega)$ from historical Raman measurementsraman in K3C60 showing broad features which derive from molecular phonons ${\rm Hg}$$1$ (orange), ${\rm Hg}$$2$ (purple), and ${\rm Hg}$$3$ and $4$ (light green). Overlain, the raw photo-susceptibility data (crimson crosses) from recent light-induced superconductivity experimentsEd_23, largely exhibiting qualitative agreement with the Raman features. (c) Schematic of the photo-susceptibility features arising from individual narrow vibration contributions in the absence of broadening. Contributions from the individual modes are shown in ${\rm Hg}$$1$ (orange), ${\rm Hg}$$2$ (purple), and ${\rm Hg}$$3$ and $4$ (light green). (d) Schematic of the photosusceptibility features arising from broadened vibrational modes showcase a breadth qualitatively consistent with what is measured in experiments.