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arXiv:2602.17238

High-temperature $η$-pairing superconductivity in the photodoped Hubbard model

Lei Geng, Aaram J. Kim, Philipp Werner

Published Feb 19, 2026• 0 citations
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Abstract

We investigate superconductivity emerging in the photodoped Mott insulating Hubbard model using steady-state dynamical mean-field theory implemented on the real-frequency axis. By employing high-order strong-coupling impurity solvers, we obtain the nonequilibrium phase diagram for photoinduced $η$-pairing superconductivity with a remarkably high effective critical temperature. We further identify a superconducting gap in the momentum-resolved spectral function and optical conductivity, providing spectroscopic signatures accessible to experiments. Our results highlight a route to a controllable form of high-temperature superconductivity in nonequilibrium strongly correlated systems, fundamentally distinct from the equilibrium $s$-wave pairing state in the attractive Hubbard model or cuprate-like $d$-wave superconductors.

DOI
10.48550/arxiv.2602.17238

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High-temperature ηηη-pairing superconductivity in the photodoped Hubbard model
We investigate superconductivity emerging in the photodoped Mott insulating Hubbard model using steady-state dynamical mean-field theory implemented on the real-frequency axis. By employing high-order strong-coupling impurity solvers, we obtain the nonequilibrium phase diagram for photoinduced ηηη-pairing superconductivity with a remarkably high effective critical temperature. We further identify a superconducting gap in the momentum-resolved spectral function and optical conductivity, providing spectroscopic signatures accessible to experiments. Our results highlight a route to a controllable form of high-temperature superconductivity in nonequilibrium strongly correlated systems, fundamentally distinct from the equilibrium sss-wave pairing state in the attractive Hubbard model or cuprate-like ddd-wave superconductors.
We show that a metastable $\ensuremath{\eta}$-pairing superconducting phase can be induced by photodoping doublons and holes into a strongly repulsive fermionic Hubbard model. The doublon-hole condensate originates from an intrinsic doublon-hole exchange interaction and does not rely on the symmetry of the half-filled Hubbard model. It extends over a wide range of doublon densities and effective temperatures. Different nonequilibrium protocols to realize this state are proposed and numerically tested. We also study the optical conductivity in the superconducting phase, which exhibits ideal metallic behavior, i.e., a delta function at zero frequency in the conductivity, in conjunction with a negative conductivity at large frequencies. These characteristic optical properties can provide a fingerprint of the $\ensuremath{\eta}$-pairing phase in pump-probe experiments.
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ηηη-pairing in metallic and particle-hole asymmetric systems
Light-induced superconducting-like states have been reported in several classes of correlated materials. From a theoretical point of view, the induction of ηηη-pairing is a promising route to nonthermal superconductivity. Numerical studies of photo-doped Mott systems revealed ηηη-pairing states with very high effective critical temperatures. These investigations were however restricted to particle-hole symmetric states in large-gap Mott insulators, while the experiments were performed on strongly correlated metallic systems. It is thus relevant to explore if ηηη-pairing also exists in non-particle-hole symmetric setups and in photo-excited metallic states. Here we use steady-state nonequilibrium dynamical mean field theory combined with a strong-coupling impurity solver up to third order to investigate this issue. We find that in the strongly correlated regime with large Mott gap, and for low effective doublon and holon temperatures, ηηη-pairing is robust against changes in the total filling and an imbalance in the doublon and holon density. An asymmetry in the effective doublon and holon temperatures can however strongly suppress the order parameter. In photo-doped metallic systems with a three-peak structure in the local density of states, ηηη-pairing can be realized in set-ups with positive doublon and holon temperatures and a population inversion in the low-energy quasi-particle band.
Understanding light-induced hidden orders is relevant for nonequilibrium materials control and future ultrafast technologies. Hidden superconducting order, in particular, has been a focus of recent experimental and theoretical efforts. In this study, we investigate the stability of light-induced $\ensuremath{\eta}$ pairing. Using a memory truncated implementation of nonequilibrium dynamical mean field theory (DMFT) and entropy-cooling techniques, we study the long-time dynamics of the photoinduced superconducting state. In the presence of coupling to a cold phonon bath, the photodoped system reaches a quasi-steady state, which can be sustained over a long period of time in large-gap Mott insulators. We show that this long-lived prethermalized state is well described by the nonequilibrium steady-state implementation of DMFT.
Superconductivity in laser-excited correlated electron systems has attracted considerable interest due to reports of light-induced superconductinglike states. Here we explore the possibility of nonthermal superconducting order in strongly interacting multiorbital Hubbard systems, using nonequilibrium dynamical mean field theory. We find that a staggered $\ensuremath{\eta}$-type superconducting phase can be realized on a bipartite lattice in the high photodoping regime, if the effective temperature of the photocarriers is sufficiently low. The $\ensuremath{\eta}$ superconducting state is stabilized by Hund coupling---a positive Hund coupling favors orbital-singlet spin-triplet $\ensuremath{\eta}$ pairing, whereas a negative Hund coupling stabilizes spin-singlet orbital-triplet $\ensuremath{\eta}$ pairing.
The finite-temperature phase diagram of the attractive Hubbard model is studied by means of the dynamical mean-field theory. We first consider the normal phase of the model by explicitly frustrating the superconducting ordering. In this case, we obtain a first-order pairing transition between a metallic phase and a paired phase formed by strongly coupled incoherent pairs. The transition line ends in a finite temperature critical point, but a crossover between two qualitatively different solutions still occurs at higher temperature. Comparing the superconducting- and the normal-phase solutions, we find that the superconducting instability always occurs before the pairing transition in the normal phase, i.e. T c > T pairing . Nevertheless, the high-temperature phase diagram at T > T c is still characterized by a crossover from a metallic phase to a preformed pair phase. We characterize this crossover by computing different observables that can be used to identify the pseudogap region, like the spin susceptibility, the specific heat and the single-particle spectral function.