Quantum-critical pairing with varying exponents

TL;DR

This paper investigates the onset temperature for pairing in cuprate superconductors near magnetic transitions, establishing a connection between the Moon-Sachdev model and a family of b3-models with varying exponents, revealing different pairing regimes.

Contribution

It demonstrates the equivalence of the Moon-Sachdev model to b3-models with varying b3, depending on proximity to magnetic criticality, and verifies the T_c formula for color superconductivity.

Findings

MS model is equivalent to b3-model with b3=1/3 in a certain parameter range.

Near the magnetic QCP, MS model corresponds to b3=0+ (b3-model with b3=0+).

The analogy allows verification of T_c formulas from color superconductivity.

Abstract

We analyse 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 \gamma-model of quantum-critical pairing with the pairing kernel \lambda (\Omega) \propto 1/\Omega^{\gamma}. We show that, over some range of parameters, the MS model is equivalent to the \gamma-model with \gamma =1/3 (\lambda (\Omega) \propto \Omega^{-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 the \gamma-model with varying \gamma >1/3, whose value depends on the distance to a magnetic transition and approaches \gamma =1 deep in a paramagnetic phase. Very near the transition, the MS model becomes equivalent to the \gamma-model with varying \gamma <1/3. Right at the magnetic QCP, the MS model is equivalent to the \gamma-model with \gamma =0+ (\lambda (\Omega) \propto \log \Omega), which is the model for color superconductivity. Using this analogy, we verified the formula for T_c derived for color superconductivity.