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arXiv:cond-mat/9911445 · Europhysics Letters (EPL)

Coherent vs . incoherent pairing in 2D systems near magnetic instability

Ar. Abanov, Andrey V. Chubukov, Alexander M. Finkel’stein

Published May 1, 2001• 125 citations
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Abstract

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 T ins 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.

DOI
10.1209/epl/i2001-00266-0

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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 T ins 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.
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We solve the problem of fermionic pairing mediated by a massless boson in the limit of large coupling constant. At weak coupling, the transition temperature is exponentially small and superconductivity is robust against phase fluctuation. In the strong coupling limit, the pair formation occurs at a temperature of the order of the Fermi energy, however, the actual transition temperature is much smaller due to phase and amplitude fluctuations of the pairing gap. Our model calculations describe superconductivity due to color magnetic interactions in quark matter and in systems close to a ferromagnetic quantum critical point with Ising symmetry. Our strong coupling results are, however, more general and can be applied to other systems as well, including the antiferromagnetic exchange in 2D used for description of the cuprates.
The origin of the pseudogap behavior, found in many high-TcT_cTc​ superconductors, remains one of the greatest puzzles in condensed matter physics. One possible mechanism is fermionic incoherence, which near a quantum critical point allows pair formation but suppresses superconductivity. Employing quantum Monte Carlo simulations of a model of itinerant fermions coupled to ferromagnetic spin fluctuations, represented by a quantum rotor, we report numerical evidence of pseudogap behavior, emerging from pairing fluctuations in a quantum-critical non-Fermi liquid. Specifically, we observe enhanced pairing fluctuations and a partial gap opening in the fermionic spectrum. However, the system remains non-superconducting until reaching a much lower temperature. In the pseudogap regime the system displays a gap-filling rather than gap-closing behavior, consistent with experimental observations. Our results provide the first unambiguous lattice model realization of a pseudogap state in a strongly correlated system, driven by superconducting fluctuations.
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Evidence that the pseudogap (PG) in a near-optimally doped Bi2_22​Sr2_22​CaCu2_22​O8+δ_{8+δ}8+δ​ sample destroys the BCS logarithmic pairing instability [1] raises again the question of the role of the PG in the high-temperature superconducting cuprates [2]. The elimination of the BCS instability is consistent with the view that the PG competes with superconductivity. However, as noted in [1], the onset of superconductivity with a Tc∼90T_c \sim 90Tc​∼90 K suggests an alternative scenario in which the PG reflects the formation of short range pairing correlations. Here, we report results obtained from a dynamic cluster quantum Monte Carlo approximation (DCA) for a 2D Hubbard model and conclude that (1) the PG, like the superconductivity, arises due to short-range antiferromagnetic correlations and (2) contrary to the usual case in which the pairing instability arises from the Cooper instability, here, the strength of the spin-fluctuations increases as the temperature decreases leading to the pairing instability.
Near a quantum-critical point in a metal strong fermion-fermion interaction mediated by a soft collective boson gives rise to incoherent, non-Fermi liquid behavior. It also often gives rise to superconductivity which masks the non-Fermi liquid behavior. We analyze the interplay between the tendency to pairing and fermionic incoherence for a set of quantum-critical models with effective dynamical interaction between low-energy fermions. We argue that superconducting T_{c} is nonzero even for strong incoherence and/or weak interaction due to the fact that the self-energy from dynamic critical fluctuations vanishes for the two lowest fermionic Matsubara frequencies ω_{m}=±πT. We obtain the analytic formula for T_{c}, which reproduces well earlier numerical results for the electron-phonon model at vanishing Debye frequency.