Superconductivity mediated by quantum critical antiferromagnetic fluctuations: The rise and fall of hot spots

TL;DR

This study investigates how quantum critical antiferromagnetic fluctuations influence superconductivity, revealing that hot spots on the Fermi surface primarily determine the transition temperature and pairing susceptibility.

Contribution

The paper combines Quantum Monte Carlo simulations and analytical calculations to identify hot spots as key to superconductivity near quantum critical points in the spin-fermion model.

Findings

Superconducting $T_c$ is governed by hot spots, not the entire Fermi surface.

$T_c$ increases with interaction strength and saturates at a crossover point.

Hot spots dominate pairing susceptibility in the studied regime.

Abstract

In several unconventional superconductors, the highest superconducting transition temperature $T_{c}$ is found in a region of the phase diagram where the antiferromagnetic transition temperature extrapolates to zero, signaling a putative quantum critical point. The elucidation of the interplay between these two phenomena - high-$T_{c}$ superconductivity and magnetic quantum criticality - remains an important piece of the complex puzzle of unconventional superconductivity. In this paper, we combine sign-problem-free Quantum Monte Carlo simulations and field-theoretical analytical calculations to unveil the microscopic mechanism responsible for the superconducting instability of a general low-energy model, called spin-fermion model. In this approach, low-energy electronic states interact with each other via the exchange of quantum critical magnetic fluctuations. We find that even in the regime of moderately strong interactions, both the superconducting transition temperature and the pairing susceptibility are governed not by the properties of the entire Fermi surface, but instead by the properties of small portions of the Fermi surface called hot spots. Moreover, $T_{c}$ increases with increasing interaction strength, until it starts to saturate at the crossover from hot-spots dominated to Fermi-surface dominated pairing. Our work provides not only invaluable insights into the system parameters that most strongly affect $T_{c}$, but also important benchmarks to assess the origin of superconductivity in both microscopic models and actual materials.