Superconducting Fluctuations in the Normal State of the Two-Dimensional Hubbard Model

TL;DR

This study uses the dynamical cluster approximation to identify the parameter regimes in the two-dimensional Hubbard model that maximize superconducting transition temperatures, revealing optimal conditions at intermediate coupling and doping levels.

Contribution

It provides a detailed analysis of superconducting fluctuations and transition temperatures in the 2D Hubbard model, highlighting the effects of interaction strength, doping, and hopping parameters.

Findings

Optimal $T_c$ occurs at intermediate coupling.

Superconducting fluctuations are strongest at intermediate doping.

Sign change in vertex contributions from repulsive to attractive with doping.

Abstract

We compute the two-particle quantities relevant for superconducting correlations in the two-dimensional Hubbard model within the dynamical cluster approximation. In the normal state we identify the parameter regime in density, interaction, and second-nearest-neighbor hopping strength that maximizes the $d_{x^2-y^2}$ superconducting transition temperature. We find in all cases that the optimal transition temperature occurs at intermediate coupling strength, and is suppressed at strong and weak interaction strengths. Similarly, superconducting fluctuations are strongest at intermediate doping and suppressed towards large doping and half-filling. We find a change in sign of the vertex contributions to $d_{xy}$ superconductivity from repulsive near half filling to attractive at large doping. $p$-wave superconductivity is not found at the parameters we study, and $s$-wave contributions are always repulsive. For negative second-nearest-neighbor hopping the optimal transition temperature shifts towards the electron-doped side in opposition to the van Hove singularity which moves towards hole doping. We surmise that an increase of the local interaction of the electron-doped compounds would increase $T_c$.