Strongly Correlated Superconductivity and Pseudogap Phase near a Multiband Mott Insulator

Near a Mott transition, strong electron correlations may enhance Cooper pairing. This is demonstrated in the dynamical mean field theory solution of a twofold-orbital degenerate Hubbard model with an inverted on-site Hund rule exchange, favoring local spin-singlet configurations. Close to the Mott insulator (which here is a local version of a valence bond insulator) a pseudogap non-Fermi-liquid metal, a superconductor, and a normal metal appear, in striking similarity with the physics of cuprates. The strongly correlated $s$-wave superconducting state has a larger Drude weight than the corresponding normal state. The role of the impurity Kondo problem is underscored.

Figure 1

Superconducting gap for $\langle n\rangle =2$ as a function of on-site repulsion for fixed coupling $J=\lambda /(2N_F)$. Increasing repulsion spoils superconductivity at large coupling. Superconductivity is instead strongly enhanced close to the Mott transition at weak coupling. The inset shows the weak coupling regime on an expanded scale, showing a much smaller gap at small $U$ compared with SCS at large $U$.

Figure 2

Drude weight as a function of $U$ at $J=0.05W$. SCS points: superconducting solution; unstable metal points: metastable solution with superconducting order parameter forced equal to zero. Note the very large Drude weight increase in the SCS pocket (magnified in the inset).

Figure 3

Single-particle DOS at $J=0.05W$ of the metallic solution for $U$ close to the MIT (superconductivity disallowed between $U=0.7$ and $U_c\simeq 0.88$). Note the pseudogap within the low-energy quasiparticle peak coexisting with the high-energy Hubbard bands. The spiky nature of the spectrum in an artifact introduced by the discrete Lanczos diagonalization.

Figure 4

Behavior of the relevant energy scales (defined in the text) close to the MIT for $J/W=0.05$ as function of $U/W$.

Figure 5

Phase diagram as a function of $U/W$ and doping $\delta =n-2$ at $J=0.05W$. The thick vertical line marks the singlet Mott insulator. The inset shows, for $U=0.92W$, the superconducting gap $\Delta$ divided by a factor ${10}^{-3}$ and the Drude weight $D$ (normalized to the noninteracting value) as functions of doping $\delta$.