@Chia2003; @Hashimoto2013; @Truncik2013] When combining with other thermodynamic and transport measurements like heat capacity,[@Movshovich2001; @An2010] thermal conductivity,[@Movshovich2001; @Izawa2001] dc magnetization,[@Tayama2002] NMR,[@Kohori2001] tunneling spectrum,[@Ernst2010] and the observation of a characteristic $(\pi,\pi,\pi)$ spin resonance mode and quasi-particle interference signal,[@Stock2008; @Allan2013; @Zhou2013; @Morr2014] CeCoIn$_{5}$ is now believed to be a nodal-$d_{x^{2}-y^{2}}$ wave superconductor, which has remarkable similarity to the well-known high-$T_{c}$ cuprate.

More recently, London penetration depth measurement of Yb-doped CeCoIn$_{5}$, i.e. Ce$_{1-x}$Yb$_{x}$CoIn$_{5}$, has been performed and unexpectedly the power-law behavior is gradually replaced by a fully gapped exponential behavior upon Yb-doping.[@Kim2015] (Note however a recent thermal conductivity measurement implies the nodal-d wave is robust and no pairing symmetry transition exists.[@Xu2015]) Such surprising experimental finding is explained to be a change of pairing symmetry and even inspires an exotic local pairing scenario involving composite molecular superfluid and Lifshitz transition of nodal Fermi surface.[@Erten2015]

However, when we try to understand the superfluid response in those heavy fermion superconductors from a theoretical point, it is unfortunate to find that in literature explicit expression of superfluid response function, particularly for microscopic model Hamiltonian, is rare despite widespread and intensive experimental exploration. (Note however, some phenomenological Fermi liquid-based arguments and superfluid density formula of composite pairing indeed 