  Motivated by recent London penetration depth measurement [H. Kim et al. Phys.
Rev. Lett. \textbf{114}, 027003 (2015)] and novel composite pairing scenario
[O. Erten, R. Flint and P. Coleman, Phys. Rev. Lett. \textbf{114}, 027002
(2015)] on Yb-doped heavy fermion superconductor CeCoIn$_{5}$, we revisit the
issue of superfluid response in microscopic heavy fermion lattice model.
However, it is found that in literature explicit expression of superfluid
response function in heavy fermion superconductor is rare. In this paper, we
make a contribution to this issue by investigating superfluid density response
function in celebrated Kondo-Heisenberg model. To be specific, we derive
corresponding formalism from an effective fermionic large-N mean-field pairing
Hamiltonian, whose pairing interaction is assumed to originate from effective
local antiferromagnetic exchange interaction. Interestingly, it is found that
physically correct superfluid density formula can only be obtained if external
electromagnetic field is directly coupled to heavy fermion quasi-particle. Such
unique feature emphasizes the key role of Kondo-screening-renormalized
quasi-particle for low-temperature/energy thermodynamics and transport
behaviors. As an important application, the theoretical result is compared to
experimental measurement in heavy fermion superconductor CeCoIn$_{5}$ and
Yb-doped Ce$_{1-x}$Yb$_{x}$CoIn$_{5}$, where the agreement is fairly good and
the transition of pairing symmetry in the latter one is explained as a simple
doping effect. In addition, the requisite formalism for the commonly
encountered nonmagnetic impurity and non-local electrodynamic effect are
developed.
