Finite-cluster study of superconductivity in the two-dimensional molecular-crystal model

Abstract

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 ${\mathit{T}}_{\mathit{c}}$ and to calculate the temperature-dependent gap function below ${\mathit{T}}_{\mathit{c}}$. 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-${\mathit{T}}_{\mathit{c}}$ 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 ${\mathit{T}}_{\mathit{c}}$ 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.