## Abstract

We analyze the onset temperature T _{p} for the pairing in cuprate superconductors at small doping, when tendency towards antiferromagnetism is strong. We consider the model of Moon and Sachdev (MS), which assumes that electron and hole pockets survive in a paramagnetic phase. Within this model, the pairing between fermions is mediated by a gauge boson, whose propagator remains massless in a paramagnet. We relate the MS model to a generic γ-model of quantum-critical pairing with the pairing kernel λ(Ωn) α 1/Ωγ/n. We show that, over some range of parameters, the MS model is equivalent to γ=1/3-model (λ(Ω) α Ω ^{-1/3}). We find, however, that the parameter range where this analogy works is bounded on both ends. At larger deviations from a magnetic phase, the MS model becomes equivalent to γ model with varying γ>1/3, whose value depends on the distance to a magnetic transition and approaches γ=1 deep in a paramagnetic phase. Very near the transition, the MS model becomes equivalent to γ model with varying γ<1/3. Right at the magnetic QCP, the MS model is equivalent to the model with λ(Ω _{n} ) α log∈Ω _{n}, which is the model for color superconductivity. Using this analogy, we verify the formula for T _{c} derived for color superconductivity.

Original language | English (US) |
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Pages (from-to) | 263-281 |

Number of pages | 19 |

Journal | Journal of Low Temperature Physics |

Volume | 161 |

Issue number | 1-2 |

DOIs | |

State | Published - Oct 2010 |

### Bibliographical note

Funding Information:Acknowledgements We thank S. Sachdev, M. Metlitskii and J. Schmalian for the interest in this work and useful comments. This work was supported by NSF DMR-0757145 and the Samsung Scholarship (E.G. Moon) and by NSF-DMR-0906953 (A.V. Ch.)

## Keywords

- Non-Fermi liquid
- Quantum phase transitions
- Superconductivity