Interplay of Pomeranchuk instability and superconductivity in the two-dimensional repulsive Hubbard model

TL;DR

This study explores how Pomeranchuk instability and d-wave superconductivity interact in the 2D Hubbard model, revealing that Fermi surface distortions can influence superconducting transition temperatures and coexistence phases.

Contribution

It demonstrates the impact of Fermi surface symmetry breaking on superconductivity and maps the conditions under which Pomeranchuk instability and superconductivity coexist or compete.

Findings

Pomeranchuk instability occurs near van Hove filling with Fermi surface distortion.

Superconductivity can coexist with Pomeranchuk distortion, changing from d-wave to (d+s)-wave.

Fermi surface distortion can enhance superconducting transition temperature in overdoped regimes.

Abstract

Interplay of Pomeranchuk instability (spontaneous symmetry breaking of the Fermi surface) and d-wave superconductivity is studied for the repulsive Hubbard model on the square lattice with the dynamical mean field theory combined with the fluctuation exchange approximation (FLEX+DMFT). We show that the four-fold symmetric Fermi surface becomes unstable against a spontaneous distortion into two-fold near the van Hove filling, where the symmetry of superconductivity coexisting with the Pomeranchuk distorted Fermi surface is modified from the d-wave pairing to (d+s)-wave. By systematically shifting the position of van Hove filling with varied second- and third-neighbor hoppings, we find that the transition temperature $T_{\rm c}^{\rm PI}$ of Pomeranchuk instability is more sensitively affected by the position of van Hove filling than the superconducting $T_{\rm c}^{\rm SC}$. This implies that the filling region for strong Pomeranchuk instability and that for strong superconducting fluctuations can be separated, and Pomeranchuk instability can appear even if the peak of $T_c^{\rm PI}$ is lower than the peak of $T_c^{\rm SC}$. An interesting observation is that the Fermi surface distortion can enhance the superconducting $T_{\rm c}^{\rm SC}$ in the overdoped regime, which is explained with a perturbation picture for small distortions.