FINITE-CLUSTER STUDY OF SUPERCONDUCTIVITY IN THE 2-DIMENSIONAL MOLECULAR-CRYSTAL MODEL

We study the singlet pairing and charge-density-wave (CDW) instabilities in the two-dimensional molecular-crystal model using diagrammatic perturbation theory and nonperturbative fermion Monte Carlo (MC) methods applied to a 36-site cluster. Migdal-Eliashberg strong-coupling theory is used to calculate susceptibilities above T(c) and to calculate the temperature-dependent gap function below T(c). These computations are performed with bare phonons as well as renormalized ones, and for a range of doping concentrations spanning the CDW phase transition. We find close agreement between the pairing susceptibility calculated within the strong-coupling approximation using bare phonons and susceptibility calculated by the fermion Monte Carlo technique. Using the above-and below-T(c) strong-coupling calculations as a guide, we argue that the fermion MC computation indicates a superconducting ground state with the highest transition temperature occurring at a doping concentration close to the CDW phase boundary. The increase in T(c) is attributed mostly to the logarithmic singularity in the density of states at half-filling. Phonon softening seems to have only a small effect according to the nonperturbative treatment.