Quantum-critical superconductivity in underdoped cuprates

– We argue that the pseudogap phase may be an attribute of the non-BCS pairing of quantum-critical, diffusive fermions near the antiferromagnetic quantum critical point. We derive and solve a set of three coupled Eliashberg-type equations for spin-mediated pairing and show that in some T range below the pairing instability, there is no feedback from superconductivity on fermionic excitations, and fermions remain diffusive despite of the pairing. We conject that in this regime, fluctuations of the pairing gap destroy the superconducting condensate but preserve the leading edge gap in the fermionic spectral function. The pseudogap behavior in underdoped cuprates is one of the most unusual and exciting features of condensed matter physics. By all experimental accounts, below optimal doping superconducting-like behavior of fermionic observables sets in at a temperature which increases with underdoping. This temperature correlates with the value of the superconducting gap at T = 0, but does not correlate with the transition temperature itself. The latter decreases with underdoping and eventually vanishes [1]. In this paper we argue that the pseudogap behavior may be a part of new, non-Fermiliquid physics associated with the pairing of fermions in the quantum-critical regime near the antiferromagnetic quantum critical point. The onset of the pairing in this regime has been recently studied by Finkel’stein and two of us (ACF) [2]. ACF demonstrated that the onset temperature T = Tins is determined by a competition between fermionic incoherence and the absence of a gap for spin excitations which mediate superconductivity [3]. Due to this competition, Tins tends to a finite value when the spin correlation length, ξ, diverges. An obvious question posed by this result is whether the pairing instability at Tins leads to true superconductivity, or only gives rise to a formation of spin singlets which still behave incoherently and hence do not superconduct. If this was the case, the phase right below Tins would be a pseudogap phase, while the actual superconductivity would emerge only at a smaller temperature. This paper is a first step in addressing this issue. We report the results of our analysis of the system behavior within the Eliashberg-type approach [4]. This approach is mean-field like in the sense that it does not include the feedback effect from the pairing modes (e.g., phase fluctuations) on fermions and spin excitations. However, it does include nontrivial physics associated with non BCS pairing in the quantum-critical regime. We show that pairing of