Claudio Castellani: Superconductivity near a multiband Mott transition

Claudio Castellani introduced a DMFT toy model, motivated by the
fullerenes in order to describe the emergence of superconductivity
near a multiband Mott transition.

Claudio began his talk by briefly reviewing the effects of strong
electronic correlations on superconductivity. He pointed out that
there are two opposing effects. First, correlations reduce he
spectral weight of the electronic states (with quasi particle weight
Z<1) and hence reduce the electronic band width from W to Z*W. This
in turn leads to an increase in the density of states from rho to
rho/Z, which should give rise to an increase in Tc. On the other
hand, the attractive pairing potential, V, is reduced to V * Z^2,
which implies a reduction in Tc. Hence, in order to increase Tc
through strong correlations, it is necessary to increase the density
of states without a reduction in the pairing potential.

Claudio then introduced a 2-band Hubbard model with interorbital J,
whose ground state possesses 2 electrons per site (Claudio also
mentioned its relation to the 2 orbital Kondo-model). Since this J
gives rise to the formation of on-site singlets, this model allows
one to study superconductivity in an RVB environment. However, the
symmetry of the resulting superconducting state is s-wave, and hence
this is not a model for the cuprate superconductors, but is likely
more applicable to the fullerenes. Claudio studied this model by
using dynamical mean-field theory (DMFT).

Claudio identified a quantum critical point of the model which
separates a Fermi-liquid regime from a pseudo-gap phase. In the
vicinity of the QCP, the superconducting Tc is enhanced, and the
physical behavior of the system is determined by two energy scales,
that of the pseudogap and that of the SC gap. For large J, Claudio
found the uusual Migdal-Eliashberg type of reduction of Tc, while
for small J, the superconducting Tc is enhanced by the Coulomb U.
Claudio pointed out that there is a Drude weight gain in the SC
state, but that in the metallic state, the Drude weight goes to zero
before the QCP is reached. Claudio identified the pseudogap state as
an unstable metallic phase.

Last, Claudio raised the question of whether superconductivity is an
instability of the pseudogap, or whether these two have no relations
at all. He stated that the processes leading ot the pseudo gap are
not competing with pairing but with coherence, in analogy with
non-pairbreaking impurities in conventional superconductors.

Thilo Kopp asked whether other interactions (besides the
interorbital J) are included in this model, which Claudio confirmed.

Catherine Pepin asked how one can make any statements about the
Kondo physics of this model within single-site DMFT. Claudio
answered that this is possible since the model is a 2 orbital Kondo
model, in which the QCP separates the Kondo-screened phase from the
unscreened phase.