In several unconventional superconductors, the highest superconducting transition temperature Tc 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-Tc 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 the 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, Tc 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 Tc, but also important benchmarks to assess the origin of superconductivity in both microscopic models and actual materials.
Bibliographical noteFunding Information:
X.W. and R.M.F. were supported by the US Department of Energy, Office of Science, Basic Energy Sciences, under Award No. DE-SC0012336. R.M.F. and X.W. thank the Minnesota Supercomputing Institute (MSI) at the University of Minnesota, where part of the numerical computations was performed. R.M.F. also acknowledges partial support from the Research Corporation for Science Advancement via the Cottrell Scholar Award, and X.W. acknowledges support from the Doctoral Dissertation Fellowship offered by the University of Minnesota. E.B. was supported by the Israel Science Foundation under Grant No. 1291/12, by the US-Israel BSF under Grant No. 2014209, by a Marie Curie career reintegration grant, and by an Alon fellowship. R.M.F. and E.B. are grateful for the hospitality of the Aspen Center for Physics, where part of this work was developed. The Aspen Center for Physics is supported by National Science Foundation Grant No. PHY-1066293.