Andreev reflection in heavy fermions and the superconducting order parameter in CeCoIn$_{5}$

Andreev reflection, a retro-reflection of an incoming electron as a hole at a normal-metal/superconductor interface, is well understood in conventional superconductors. For heavy-fermion superconductors, the microscopic consequences of the heavy electronic mass remain an open question. According to the Blonder-Tinkham-Klapwijk (BTK) theory, no Andreev process is allowed because of the large mismatch in the Fermi velocities [1]. However, conductance enhancement due to Andreev reflection, albeit reduced, has been frequently observed in heavy-fermion superconductors [2]. In this talk, I will present such conductance spectra obtained along three different crystallographic orientations of the heavy-fermion superconductor CeCoIn$_{5}$ [3]. Qualitative analysis using the extended BTK model shows the first spectroscopic evidence for $d_{\mbox{x}^2-\mbox{y}^2} $-wave (instead of $d_{xy}$-wave) symmetry, resolving the controversy over the node locations. In order to explain the reduced Andreev signal and the conductance asymmetry, both commonly observed in heavy-fermion superconductors, we propose a conductance model based on the two-fluid phenomenology [4] and an assumed energy-dependent density of states. I will discuss the significance of this model and possible clues for developing it into a microscopic theory. [1] G. E. Blonder, M. Tinkham, and T. M. Klapwijk, Phys. Rev. B \textbf{25}, 4515 (1982); G. E. Blonder and M. Tinkham, \textit{ibid}. \textbf{27}, 112 (1983). [2] Yu. G. Naidyuk and I. K. Yanson, J. Phys.: Condens. Matter \textbf{10}, 8905 (1998). [3] W. K. Park \textit{et al}., arXiv:0709.1246 (submitted to Phys. Rev. Lett.). [4] S. Nakatsuji, D. Pines, and Z. Fisk, Phys. Rev. Lett. \textbf{92}, 016401 (2004). This work is done in collaboration with L. H. Greene, H. Stalzer, J. L. Sarrao, J. D. Thompson, Z. Fisk, and P. Canfield.