Coherent Vs Incoherent Pairing in 2d Systems near Mag- Netic Instability

– We study the superconductivity in 2D fermionic systems near antiferromagnetic instability, assuming that the pairing is mediated by spin fluctuations. This pairing involves fully incoherent fermions and diffusive spin excitations. We show that the competition between fermionic incoherence and strong pairing interaction yields the pairing instability temperature Tins which increases and saturates as the magnetic correlation length ξ → ∞. We argue that in this quantum-critical regime the pairing problem is qualitatively different from the BCS one. In this communication we analyse the pairing problem in 2D fermionic systems near antiferromagnetic instability. Our key goal is to investigate whether or not the closeness to antiferromagnetism is in conflict with the magnetically mediated d−wave pairing. This problem is rather peculiar as on one hand the d−wave pairing amplitude increases at approaching the AFM instability due to softening of spin fluctuations [1], while on the other hand, strong spin-mediated interaction destroys fermionic coherence [2,3] and therefore damages the ability of fermions to form Cooper pairs. We demonstrate that the competition between strong pairing interaction and the destruction of fermionic coherence yields a pairing instability at a temperature Tins which increases and saturates when the magnetic correlation length ξ → ∞. We show that under certain conditions, Tins is universal in the sense that it does not depend on the details of the electronic dispersion at energies comparable to the fermionic bandwidth W , and is determined by fermions located in a narrow region near hot spots the points at the Fermi surface separated by the antiferromagnetic momentum Q. We assume in this paper that the Fermi surface does contain hot spots. We believe that the results of our analysis may be applicable to both cuprates and heavy fermion materials. For high Tc cuprates, our results may be useful for understanding of the pseudogap physics in the underdoped regime, where the data show that the temperature when the system first displays superconducting precursors saturates at the lowest dopings [4]. We conject that our Tins may be the onset of the pseudogap behavior, while the actual superconducting transition occurs at a smaller temperature. For heavy fermion materials, our result may help understand the close correlation between the appearance of the superconductivity and an antiferromagnetic instability [5].