f-electron mediated Cooper Pairing in CeCoIn$_5$*

Recent experimental breakthroughs in scanning tunneling spectroscopy have made it possible to probe how the complex electronic structure of the heavy fermion compound CeCoIn$_5$ evolves with decreasing temperature, eventually leading to the emergence of an unconventional superconducting state [1,2]. Using a recently developed theoretical model for quasi-particle interference (QPI) spectroscopy in heavy fermion materials [3,4], we demonstrate that the experimental QPI data are consistent with a superconducting order parameter of $d_{x^2 y^2}$-symmetry, possessing a complex, multi-band momentum space structure [1]. Furthermore, we show that the unprecedented insight into the complex electronic structure of CeCoIn$_5$ above $T_c$ opens a new path for identifying quantitatively the superconducting pairing potential, arising from the strong antiferromagnetic correlations in the heavy $f$-band [5]. Using this pairing potential to solve the multi-band superconducting gap equations provides us with a series of quantitative predictions for the critical temperature, the momentum space structure of the superconducting gaps, the phase sensitive QPI signature of the $d_{x^2 y^2}$ pairing symmetry, the spin-lattice relaxation rate, and the form of the magnetic ``spinresonance.'' The quantitative agreement between these predictions and the measured properties of superconducting CeCoIn$_5$ provides strong evidence for Cooper pairing being mediated by $f$-electron magnetism. \\[4pt] [1] M. P. Allan, F. Massee, D. K. Morr, J. van Dyke, A.W. Rost, A. P. Mackenzie, C. Petrovic and J. C. Davis, Nature Physics 9, 468 (2013).\\[0pt] [2] B.B. Zhou, S. Misra, E.H. da Silva Neto, P. Aynajian, R.E. Baumbach, J.D. Thompson, E.D. Bauer, and A. Yazdani, Nature Physics, 9, 474 (2013)\\[0pt] [3] F. Parisen~Toldin, J. Figgins, S. Kirchner, and D.K. Morr, Phys. Rev. B 88, 081101(R) (2013) \\[0pt] [4] T. Yuan, J.Figgins, and D.K. Morr, Phys. Rev. B 86, 035129 (2012). \\[0pt] [5] J. van Dyke F. Massee, M. P. Allan, J. C. Davis, C. Petrovic and D. K. Morr, submitted (2013).