to study the superfluid response in a kind of typical heavy fermion superconductor CeCoIn$_{5}$. To meet with the realistic experimental measurement, we fix model parameters as $t=-1$, $t'=0.3$, $J_{K}=2$, $J_{H}=0.6$, $V=-0.2965$, $\chi=0.2222$ and $n_{c}=0.9$,[@Zhong2015epjb] thus the resulting normal state Fermi surface is shown in Fig. \[fig:pairingstrength\], which mimics the multi-Fermi surface structure observed in ARPES measurement.[@Koitzsch2009; @Jia2011]

![\[fig:pairingstrength\] Mean-field Fermi surface (bold black line), $d_{x^{2}-y^{2}}$ (Left) and extended-s (Right) wave pairing function in square lattice Brillouin zone.](wave.eps){width="0.8\columnwidth"}

Performing calculation with Eq. \[eq11\] and assuming $d_{x^{2}-y^{2}}$-wave pairing, we compare our theoretical result to experimental data in Fig. \[fig:10\]. From Fig. \[fig:10\] we see that our theory is good consistent with the global behavior in microwave surface impedance measurements of Ref.  and also agrees with our previous work.[@Zhong2015epjb] Particularly, the observed low-temperature linear/power-law behavior of superfluid density is well reproduced by our theoretical model with only assumption of $d_{x^{2}-y^{2}}$-wave symmetry.[@Ormeno2002; @Ozcan2003; @Chia2003; @Hashimoto2013; @Truncik2013]

Issues on Ce$_{1-x}$Yb$_{x}$CoIn$_{5}$
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Next, it is interesting to understand the possible pairing symmetry transition in Yb-doped CeCoIn$_{5}$, which is suggested by recent superfluid density measurement and inspires an exotic local electron pairing scenario.[@Kim2015; @Erten2015] Effectively, Yb-doping adds extra electron carrier into CeCoIn$_{5}$, thus density of charge carrier 