Pairing in quantum critical systems: Transition temperature, pairing gap, and their ratio

Article

关键词: STRONG-COUPLING LIMIT;    SUPERCONDUCTIVITY;   

DOI  :  10.1103/PhysRevB.99.014502

来源: SCIE

【 摘 要 】

We compute the ratio of the pairing gap Delta at T = 0 and T-c for a set of quantum-critical models in which the pairing interaction is mediated by a gapless boson with local susceptibility chi(Omega) proportional to 1/vertical bar Omega vertical bar(gamma) (the gamma model). The limit gamma = 0+ [chi (Omega) = log vertical bar Omega vertical bar] describes color superconductivity, and models with gamma > 0 describe superconductivity in a metal at the onset of charge or spin order. The ratio 2 Delta/T-c has been recently computed numerically for 0 < gamma < 2 within Eliashberg theory and was found to increase with increasing gamma [T.-H. Lee et al., Phys. Rev. Lett. 121, 187003 (2018)]. We argue that the origin of the increase is the divergence of 2 Delta/T-c at gamma = 3. We obtain an approximate analytical formula for 2 Delta/T-c for gamma <= 3 and show that it agrees well with the numerics. We also consider in detail the opposite limit of small gamma. Here we obtain the explicit expressions for T-c and Delta, including numerical prefactors. We show that these prefactors depend on fermionic self-energy in a rather nontrivial way. The ratio 2 Delta/T-c approaches the BCS value 3.53 at gamma -> 0.

【 授权许可】

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