Conserving approximations for the attractive Holstein and Hubbard models

Supersolid phase accompanied by a quantum critical point in the intermediate coupling regime of the Holstein model

We reveal that electron-phonon systems described by the Holstein model on a bipartite lattice exhibit, away from half filling, a supersolid (SS) phase characterized by coexisting charge order (CO) and superconductivity (SC), and an accompanying quantum critical point (QCP). The SS phase, demonstrated by the dynamical mean-field theory with a quantum Monte Carlo impurity solver, emerges in the intermediate-coupling regime, where the peak of the Tc dome is located and the metal-insulator crossover occurs. On the other hand, in the weak- and strong-coupling regimes the CO-SC boundary is of first order with no intervening SS phases. The QCP is associated with the continuous transition from SS to SC and characterized by a reentrant behavior of the SS around it. We further show that the SS-SC transition is hallmarked by diverging charge fluctuations and a kink (peak) in the superfluid density.

Polaron crossover and bipolaronic metal-insulator transition in the half-filled Holstein model

The formation of a finite-density polaronic state is analyzed in the context of the Holstein model using the dynamical mean-field theory. The spinless and spinful fermion cases are compared to disentangle the polaron crossover from the bipolaron formation. The exact solution of dynamical mean-field theory is compared with weak-coupling perturbation theory, noncrossing (Migdal), and vertex correction approximations. We show that polaron formation is not associated with a metal-insulator transition, which is instead due to bipolaron formation.

Strong superconductivity with local Jahn-Teller phonons in C60 solids

We analyze fulleride superconductivity at experimental doping levels, treating the electron-electron and electron-phonon interactions on an equal footing, and demonstrate that the Jahn-Teller phonons create a local (intramolecular) pairing which is surprisingly resistant to the Coulomb repulsion, despite the weakness of retardation in these low-bandwidth systems. The requirement for coherence throughout the solid then yields a very strong doping dependence to T(c), one consistent with experiment and much stronger than expected from standard Eliashberg theory.

High T(c) superconductivity in MgB2 by nonadiabatic pairing

The evidence for the key role of the sigma bands in the electronic properties of MgB2 points to the possibility of nonadiabatic effects in the superconductivity of these materials. These are governed by the small value of the Fermi energy due to the vicinity of the hole doping level to the top of the sigma bands. We show that the nonadiabatic theory leads to a coherent interpretation of T(c) = 39 K and the boron isotope coefficient alphaB = 0.30 without invoking very large couplings and it naturally explains the role of the disorder on T(c). It also leads to various specific predictions for the properties of MgB2 and for the material optimization of these types of compounds.