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

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.

Figures (4)

• Figure 1: (Effective) superconducting transition temperatures versus carrier doping for chemically and photodoped Hubbard systems. Gray circles and line: $d$-wave transition temperatures of the repulsive Hubbard model at $U=7t$ from DCA calculations in Ref. Dong2019. Light- and dark-red squares: DMFT results for the attractive Hubbard model at $U=-16t$ from NCA and OCA; purple filled squares: TOA result for $U=-7t$. Competing charge order is suppressed. Crosses: photodoped Hubbard model solved within nonequilibrium DMFT using NCA (light blue), OCA (blue), and TOA (dark blue).
• Figure 2: Local and momentum-resolved spectra of the photodoped Hubbard model at $T^\text{eff}=1195\,\mathrm{K}$ for a fixed photodoping level corresponding to $\omega_F=3.5\,\mathrm{eV}$ ($\delta \approx 0.4$). Top panels: superconducting solution. Left: momentum-resolved spectral function along the high-symmetry path $\Gamma$--$X$--$M$--$\Gamma$; the inset shows a magnified view near $\omega_F=3.5\,\mathrm{eV}$ (red dashed line), highlighting the gap opening. Right: corresponding local spectral function together with the occupation. Bottom panels: results obtained for identical parameters but with the anomalous component suppressed (same color scale). For comparison, in the right panel, the superconducting local spectrum is overlaid as a gray dash-dotted line.
• Figure 3: (a) Imaginary parts of the retarded normal and anomalous self-energies, $\Sigma^{\mathrm{N}}(\omega)$ (solid lines) and $\Sigma^{\mathrm{A}}(\omega)$ (dashed lines), near $\omega=-3.5\,\mathrm{eV}$ for representative $\eta$-pairing superconducting states. Results obtained with NCA, OCA, and TOA are shown in blue, orange, and green, respectively, at $T^\text{eff}=1041\,\mathrm{K}$ (NCA, $T_c^{\mathrm{eff}}=1060\,\mathrm{K}$), $1413\,\mathrm{K}$ (OCA, $T_c^{\mathrm{eff}}=1444\,\mathrm{K}$), and $1195\,\mathrm{K}$ (TOA, $T_c^{\mathrm{eff}}=1414\,\mathrm{K}$). For the TOA result, the dash-dotted green line additionally shows $\text{Im}[\Sigma^{\mathrm{N}}(\omega)-\Sigma^{\mathrm{A}}(\omega)$]. All systems are close to the causality-violating regime. For comparison, the normal self-energy obtained with TOA under identical parameters but with pairing suppressed is shown in gray. (b) Momentum-resolved spectral function for the $\eta$-pairing state shown in Fig. \ref{['fig_dispersion']}. Dotted lines indicate the quasiparticle band determined from $\omega-\varepsilon_{\mathbf{k}}-\mathrm{Re}\,\Sigma^{N}(\omega) +\mathrm{Re}\,\Sigma^{A}(\omega)=0$. Black dots include $\mathrm{Re}\,\Sigma^{A}(\omega)$, red dots exclude it, and gray dots correspond to the normal-state solution.
• Figure 4: Optical conductivity of the photodoped Hubbard model for the same parameters as in Fig. \ref{['fig_dispersion']}. (a) Real part of the optical conductivity, $\mathrm{Re}\,\sigma(\omega)$, excluding the zero-frequency $\delta$-peak contribution. (b) Imaginary part of the optical conductivity, $\mathrm{Im}\,\sigma(\omega)$. The low-frequency behavior is shown in the insets on a logarithmic frequency scale. Blue lines correspond to the $\eta$-pairing superconducting state, while red lines show the normal-state results obtained by suppressing the anomalous component.