Superconductivity in Cuprates through Loop Current Fluctuations

The quantum-critical fluctuations of the loop-current order parameter discovered [1] in underdoped cuprates has been derived [2] recently to be of the phenomenological form proposed to produce the marginal fermi-liquid [3]properties in the normal state. The coupling function of these fluctuations to fermions is calculated and an effective particle-particle scattering through exchange of such fluctuations is generated. Partial wave decomposition of this scattering shows attractive interaction in the d-wave pairing channel. The coupling constant and the cut-off of the fluctuations is used to estimate the order of magnitude of $T_c$. Variation of $T_c$ with hole density is also discussed. [1] C.M. Varma, Phys. Rev. {\bf B73}, 155113 (2006); B. Fauque et al., Phys. Rev. Lett, {\bf 96}, 197001 (2006); A. Kaminski, et al., Nature {\bf 416}, 610 (2002). [2] Vivek Aji and C. M. Varma, cond-mat/0610646. [3] C.M. Varma, et al. Phys. Rev. Lett., {\bf 63}, 1996 (1989).