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

Abstract

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 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.

Hierarchy of energy scales in an O(3) symmetric antiferromagnetic quantum critical metal: A Monte Carlo study

“…At the hot spots, and for small λ, one can estimate the energy scale of the onset of superconductivity, T c , by solving the Eliashberg equation for the superconducting vertex in the Landau-damping regime, where self-energy corrections are negligible. For our model (1) this predicts [18] the superconducting susceptibility to diverge at a scale Note that the energy scales T c and Ω f are both of the order O( λ 2 N ) and thus there is a priori no parametrically large separation between a non-Fermi liquid and a superconducting regime.…”

“…4). By estimating when the dynamically generated contributions to the action dominate over bare ones one then finds [5,15,18,22] for the energy scale Ω b…”

“…This relation has been numerically confirmed for a generic Fermi surface coupled to an O(2) order parameter in Refs. [18,37]. Anticipating that superconductivity arising from fermions at the hotspots, Eq.…”

“…Perhaps the most prominent feature in those materials is an extended phase of high temperature superconductivity, which is generally observed in the vicinity of antiferromagnetic order. It has been proposed [9][10][11][12][13][14][15][16] and numerically demonstrated [17][18][19][20][21] that nearly-quantum critical fluctuations can mediate unconventional superconductivity and anomalously enhance the transition temperature T c . However, an in-depth understanding of this universal mechanism still remains highly desirable.…”

Fate of superconductivity in disordered Dirac and semi-Dirac semimetals

“…In the past several decades, this approach has been widely applied to investigate the non-perturbative phenomenon of dynamical symmetry breaking in high-energy physics [141,142], the dynamical chiral symmetry breaking in three-dimensional quantum electrodynamic (QED 3 ) [143][144][145][146] which is effective model in several important condensed matter systems, the excitonic insulating transition in various SM materials [41,67,[147][148][149][150][151][152][153][154][155][156]. Moreover, the DSEs approach has been applied to study the interplay of non-Fermi liquid behavior and SC pairing in various strongly correlated systems [157][158][159][160][161][162][163][164][165][166][167][168][169][170]. The most noticeable advantage of DSEs approach is that it provides a non-perturbative framework to quantitatively calculate various physical quantities, such as the Landau damping rate, disorder scattering rate, and SC gap etc., by incorporating several types of interactions in a self-consistent manner.…”