Andreev Reflection in Heavy-Fermion Superconductors and Order Parameter Symmetry in ${\mathrm{CeCoIn}}_5$

Differential conductance spectra are obtained from nanoscale junctions on the heavy-fermion superconductor ${\mathrm{CeCoIn}}_5$ along three major crystallographic orientations. Consistency and reproducibility of characteristic features among the junctions ensure their spectroscopic nature. All junctions show a similar conductance asymmetry and Andreev reflectionlike conductance with a reduced signal ($\sim 10\%–13\%$), both commonly observed in heavy-fermion superconductor junctions. Analysis using the extended Blonder-Tinkham-Klapwijk model indicates that our data provide the first spectroscopic evidence for $d_{x^2-y^2}$ symmetry. To quantify our conductance spectra, we propose a model by considering the general phenomenology in heavy fermions, the two-fluid behavior, and an energy-dependent density of states. Our model fits to the experimental data remarkably well and should invigorate further investigations.

Figure 1

Normalized conductance spectra of ${\mathrm{CeCoIn}}_5/\mathrm{Au}$ junctions (a) along (001) (after Ref. 6) and (b) along (110) orientations. Data are shifted vertically for clarity. Note the temperature evolution of the background conductance, whose asymmetry is quantified in (c) by the ratio between conductance values at $-2\mathrm{mV}$ and at $+2\mathrm{mV}$ in (a). The inset is a semilogarithmic plot ($T^{*}$ is the HF coherence temperature). Junctions along three orientations are compared in (d) at $\sim 400\mathrm{mK}$ and in (e) at $\sim 1.5\mathrm{K}$.

Figure 2

Comparison of conductance data: (a) the (100) and (b) the (110) junctions. (c),(d) Calculated conductance curves using the $d$-wave BTK model ($\Gamma =0$ and $T=0$) for antinodal and nodal junctions, respectively. (e),(f) Magnetic field dependence for the (100) junction at 400 mK and the (110) junction at 420 mK, respectively.

Figure 3

(a) Normal state conductance spectra of the (001) junction, whose features are reproduced qualitatively by the simulated Lorentzian DOS curves in (b).

Figure 4

(a) Best- fit to the data using our modified BTK model. (b) Comparison of the data with calculated DOS curves. Right-hand inset: Fano lines simulated by $f(ϵ)=(q_F+ϵ{)}^2/(1+{ϵ}^2)$, where $q_F$ is the Fano factor and $ϵ$ normalized energy. Left-hand inset: Representative conductance data of Fano line shape taken with Al tips.