High-temperature $η$-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 $η$-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.

💡 Research Summary

The authors investigate the emergence of superconductivity in a photodoped Mott‑insulating Hubbard model using steady‑state dynamical mean‑field theory (DMFT) formulated on the real‑frequency axis. By applying a strong laser pulse across the Mott gap, doublon–holon pairs are generated; because recombination is strongly suppressed in the large‑U regime, these carriers form a long‑lived nonequilibrium steady state characterized by an effective photodoping concentration δ. The key idea is that in the strong‑coupling limit the low‑energy effective Hamiltonian contains a ferromagnetic η‑spin exchange term, H_eff = (4t²/U)∑⟨ij⟩(S_i·S_j − η_i·η_j), which favors staggered η‑pairing order.

To treat this problem quantitatively the authors employ DMFT with a self‑consistent Anderson impurity model solved directly on the real‑frequency axis. They develop a third‑order strong‑coupling impurity solver (TOA) based on quantics tensor cross interpolation, which goes beyond the conventional non‑crossing (NCA) and one‑crossing (OCA) approximations. The TOA respects the causality constraint Im Σ_N(ω) ≥ Im Σ_A(ω) for the normal (Σ_N) and anomalous (Σ_A) self‑energies, a condition that NCA/OCA violate near the superconducting transition, leading to numerical instabilities.

The nonequilibrium phase diagram (Fig. 1) shows a dome‑shaped dependence of the effective critical temperature T_eff^c on δ. For a representative interaction U = 16t, T_eff^c exceeds room temperature already at δ ≈ 0.1 and reaches values of order 1500 K near optimal doping. These temperatures are comparable to, or even higher than, those obtained for the equilibrium attractive Hubbard model (s‑wave) with U = −16t, demonstrating that photodoping can generate an effective attraction of similar magnitude via η‑pairing.

Spectral signatures are examined in Fig. 2. In the η‑pairing state the momentum‑resolved spectral function displays sharp quasiparticle peaks near the shifted Fermi levels ±ω_F, and a clear gap opens at the effective Fermi energy, redistributing spectral weight. By contrast, the same parameters with the anomalous component suppressed yield a metallic spectrum without a gap. The gap is also reflected in the local density of states and in the occupation function.

Self‑energy analysis (Fig. 3) reveals that the TOA produces well‑separated normal and anomalous components. Near the gap edge the difference Im