Non-equilibrium superconductivity in driven alkali-doped fullerides

Abstract: We investigate the formation of non-equilibrium superconducting states in driven alkali-doped fullerides A$3$C${60}$. Within a minimal three-orbital model for the superconductivity of these materials, it was recently demonstrated theoretically that an orbital-dependent imbalance of the interactions leads to an enhancement of superconductivity at equilibrium [M. Kim et al. Phys. Rev. B 94, 155152 (2016)]. We investigate the dynamical response to a time periodic modulation of this interaction imbalance, and show that it leads to the formation of a transient superconducting state which survives much beyond the equilibrium critical temperature $T_c$. For a specific range of modulation frequencies, we find that the driving reduces superconductivity when applied to a superconducting state below $T_c$, while still inducing a superconducting state when the initial temperature is larger than $T_c$. These findings reinforce the relevance of the interaction-imbalance mechanism as a possible explanation of the recent experimental observation of light-induced superconductivity in alkali-doped fullerenes.

• The paper demonstrates that time-periodic, orbital-dependent modulation can dynamically induce and control superconductivity in alkali-doped fullerides.
• It employs a time-dependent Gutzwiller variational method on a three-band Hubbard-Kanamori model to capture resonant pair-breaking effects and transient superconducting order.
• Results reveal that driving frequency and modulation amplitude critically determine whether superconductivity is enhanced above or suppressed below the equilibrium critical temperature.

Non-equilibrium Superconductivity in Driven Alkali-Doped Fullerides

Introduction and Motivation

This work presents an in-depth study of non-equilibrium superconductivity in alkali-doped fullerides, focusing on A$_3$C$_{60}$ compounds subjected to periodic modulation of orbital-dependent electronic interactions. The context stems from experimental observations of light-induced superconducting-like responses in K$_3$C$_{60}$ above the equilibrium critical temperature ($T_c$), which cannot be fully reconciled with traditional theories relying on simple enhancement of the effective SC coupling.

By employing a time-dependent Gutzwiller variational approach applied to a three-band Hubbard-Kanamori model with negative Hund's coupling, the paper investigates how transient SC can be dynamically stabilized by optical excitation of specific phonon modes, most notably the $T_{1u}$ intramolecular vibrations.

Model and Theoretical Approach

The physical model comprises three half-filled $t_{1u}$ orbitals on the C$_{60}$ molecule, with on-site interactions exhibiting an inversion of Hund’s coupling due to Jahn-Teller effects. At equilibrium, all orbitals experience the same Coulomb repulsion $U$. Upon excitation of odd-parity vibrational modes (specifically $T_{1u}$), the electron-phonon coupling induces both a reduction and differentiation of the interactions, leading to a time- and orbital-dependent modulation:

$$U_{x,y}(t) = U - r(t) \frac{\delta U}{2}(1 - \cos 2\Omega t), \quad U_z(t) = U$$

where $\Omega$ is the driving frequency, and $r(t)$ parameterizes the onset of the modulation.

Non-equilibrium dynamics are treated with the time-dependent Gutzwiller approximation (tdGA), generalized to handle multi-band superconducting correlations at finite temperature. This variational technique is crucial for capturing the feedback between local correlations and the macroscopic SC order parameter out of equilibrium, substantially beyond what static mean-field or Hartree-Fock schemes can describe.

Dynamics of the Superconducting State

Simulations track the evolution of the SC order parameter following the introduction of the driving, for initial states both below and above $T_c$.

At select frequencies—specifically $\Omega = 0.1875~\text{eV}$—the periodic modulation not only enhances the SC order below $T_c$ but also induces a finite SC order above $T_c$. This is consistent with a scenario where the average interaction imbalance raises the effective $T_c$ (Figure 1).

Figure 1: Dynamics and temperature dependence of the global SC order parameter for different driving frequencies, highlighting regimes where SC is suppressed below $T_c$ but induced above $T_c$.

However, this behavior is strongly non-monotonic with respect to the driving frequency. Lowering the modulation to $\Omega=0.15~\text{eV}$ leads to a suppression of SC below $T_c$ while still enabling a transient SC above $T_c$. The order parameter dynamics for distinct orbitals and frequencies further elucidate that at intermediate driving frequencies, the modulation can induce resonant pair-breaking, rapidly suppressing the SC order (Figure 2).

Figure 2: Zero-temperature evolution of individual orbital SC order parameters under various driving frequencies, compared to the dynamics with a sudden, constant interaction imbalance.

Frequency and Resonance Effects

A key finding is the existence of a frequency window ($$0.09~\text{eV} \lesssim \Omega \lesssim 0.16~\text{eV}$$) where dynamic energy absorption via resonant excitation of intra-orbital doublons leads to significant suppression of the SC state, even when the static (unmodulated) interaction imbalance would otherwise enhance SC (Figure 3).

Figure 3: (a) Stationary zero-temperature SC order parameter versus driving frequency; (b)-(d) dynamics of orbital double occupancies and (e) internal energy, establishing the link between resonant excitations and SC suppression.

The analysis reveals that the suppression correlates with the resonance between the driving frequency $2\Omega$ and the spectrum of electronic excitations associated with non-equilibrium doublon dynamics. The energy absorption at resonance results in robust pair-breaking, overwhelming the beneficial effect of the averaged interaction imbalance.

Outside this resonant energy absorption window, at both low and high frequencies, the SC order follows the expectations from equilibrium considerations: enhancement for high-frequency driving, and modest enhancement (or reduced suppression) for slow ramps, with minimal energy absorption.

Amplitude Dependence and Experimental Relevance

The amplitude $\delta U$ of the induced interaction imbalance directly controls the enhancement of the SC order. Larger $\delta U$ results in more pronounced effects, mirroring experimental trends where high incident laser fluence (which drives larger phonon displacements) is required to observe robust transient SC signals (Figure 4).

Figure 4: Dependence of the SC enhancement effect on the amplitude of the interaction imbalance for fixed driving frequency, in correspondence with fluence-dependent experimental observations.

The theoretical framework is consistent with scenarios where the primary effect of light is the excitation of $T_{1u}$ phonons, whose coupling naturally breaks orbital degeneracy in the local Coulomb interaction. Notably, the model reproduces the lack of enhancement or even suppression of SC below $T_c$ and the existence of transient SC above $T_c$, both seen experimentally but not explained by models based solely on uniform pairing enhancement.

Implications and Outlook

The results demonstrate that the interplay between light-induced interaction imbalance and the resonant excitation of non-equilibrium doublons fundamentally governs the observed non-equilibrium superconducting response in alkali-doped fullerides. The findings bridge the gap between transient light-induced SC and intrinsic multi-orbital correlation effects, revealing regimes where SC can be transiently stabilized well above equilibrium $T_c$, and others where energy absorption quenches the order even for states initially below $T_c$.

Future experimental work—such as alkali substitution (e.g., Cs$_3$C$_{60}$ for a broader phase diagram exploration) and detailed pump-frequency dependence studies—could further validate the theory. Additional microscopic mechanisms, possibly involving direct electronic excitations, merit scrutiny but the presented framework establishes the orbital-selective interaction imbalance mechanism as a leading explanation.

Conclusion

This study establishes that time-periodic, orbital-asymmetric interaction modulation—realizable through selective optical phonon excitation—can generate non-equilibrium superconductivity in alkali-doped fullerides. The interplay between enhanced pairing and resonant energy absorption via doublon dynamics creates rich, non-trivial SC responses that match salient experimental observations: SC can both be induced above equilibrium $T_c$ and suppressed below it, contingent on driving parameters. These insights advance the theoretical understanding of photoinduced SC states and identify new dynamical regimes accessible in strongly correlated molecular superconductors.

(1702.04675)