Evolution of the Superconductivity Dome in the two dimensional Hubbard Model

TL;DR

This study uses advanced quantum Monte Carlo simulations to map out how the superconducting dome evolves in the phase diagram of the two-dimensional Hubbard model, revealing the roles of doping, next-nearest-neighbor hopping, and spin fluctuations.

Contribution

It provides a detailed analysis of the superconducting dome's evolution, including the effects of t' and the dominance of spin fluctuations, using large-scale simulations and parquet decomposition.

Findings

Superconducting transition temperature peaks near doping n≈0.85.

The irreducible pairing vertex is enhanced as t' becomes negative.

Spin fluctuations dominate the pairing mechanism in the dome region.

Abstract

In a recent publication [Chen et al., Phys. Rev. B 86, 165136 (2012)], we identified a line of Lifshitz transition points separating the Fermi liquid and pseudogap regions in the hole-doped two dimensional Hubbard model. Here we extend the study to further determine the superconducting transition temperature in the phase diagram. By means of large-scale dynamical cluster quantum Monte Carlo simulations, we are able to identify the evolution of the d-wave superconducting dome in the hole-dope side of the phase diagram, with next-nearest-neighbor hopping (t'), chemical potential and temperature as control parameters. To obtain the superconducting transition temperature Tc, we employ two-particle measurements of the pairing susceptibilities. As t' goes from positive to negative values, we find the d-wave projected irreducible pairing vertex function is enhanced, and the curvature of its doping dependence changes from convex to concave, which fixes the position of the maximum superconducting temperature at the same filling (n close to 0.85) and constraints the dome from precisely following the Lifshitz line. We furthermore decompose the irreducible vertex function into fully irreducible, charge and spin components via the parquet equations, and consistently find that the spin component dominates the pairing vertex function in the doping range where the dome is located. Our investigations deepen the understanding of the phase diagram of the two dimensional Hubbard model.