Andreev reflection and order parameter symmetry in heavy-fermion superconductors: The case of CeCoIn₅

We review the current status of Andreev reflection spectroscopy on the heavy fermions, mostly focusing on the case of CeCoIn₅, a heavy-fermion superconductor with a critical temperature of 2.3 K. This is a well-established technique to investigate superconducting order parameters via measurements of the differential conductance from nanoscale metallic junctions. Andreev reflection is clearly observed in CeCoIn₅ as in other heavy-fermion superconductors. Considering the large mismatch in Fermi velocities, this observation seemingly appears to disagree with the Blonder-Tinkham-Klapwijk (BTK) theory. The measured Andreev signal is highly reduced to the order of maximum ∼13% compared to the theoretically predicted value (100%). The background conductance exhibits a systematic evolution in its asymmetry over a wide temperature range from above the heavy-fermion coherence temperature down to well below the superconducting transition temperature. Analysis of the conductance spectra using the extended BTK model provides a qualitative measure for the superconducting order parameter symmetry, which is determined to be the d_x²-y² wave in CeCoIn ₅. It is found that existing models do not quantitatively account for the data, which we attribute to the intrinsic properties of the heavy fermions. A substantial body of experimental data and extensive theoretical analysis point to the existence of two-fluid components in CeCoIn₅ and other heavy-fermion compounds. A phenomenological model is proposed employing a Fano interference effect between two conductance channels in order to explain both the conductance asymmetry and the reduced Andreev signal. This model appears plausible not only because it provides good fits to the data but also because it is highly likely that the electrical conduction occurs via two channels, one into the heavy-electron liquid and the other into the conduction electron continuum. Further experimental and theoretical investigations will shed new light on the mechanism of how the coherent heavy-electron liquid emerges out of the Kondo lattice, a prototypical strongly correlated electron system. Unresolved issues and future directions are also discussed.