exist.[@Varma1986; @Coleman1999]) So, in the present study, we focus on this issue by investigating superfluid density response function in the celebrated microscopic Kondo-Heisenberg model.[@Coleman1989] Specifically, we give a detailed derivation on corresponding formalism from an effective fermionic large-N mean-field pairing Hamitonian,[@Liu2012; @Liu2014] whose pairing interaction is alternatively assumed to originate from effective local antiferromagnetic exchange interaction,[@Hu2012] though more conventional antiferromagnetic spin-fluctuation-exchange and resonance-valence-bond (RVB) theory give rise to identical effective pairing Hamiltonian.[@Coleman1989; @Liu2012; @Scalapino2012; @Anderson2004; @Lee2006; @Zhong2015epjb]

Importantly, we find only if external electromagnetic field is assumed to directly couple to heavy fermion quasi-particle rather than the bare conduction electron or local moment, the physically correct superfluid density formula can be obtained without any unsatisfactory breakdown. (See also Fig. \[fig:ansatz\].) Generally, this feature underlies the fact that when considering low-temperature/energy thermodynamics and transport, the physical fermionic excitation should be the (composite) heavy fermion quasi-particle,[@Coleman] which results from nontrivial renormalization of collective Kondo screening effect. For superfluid density response considered in the present work, to match the temperature/doping evolution of superconducting heavy quasi-particle in superfluid density formula, characteristic quantities like effective velocity and mass have to be the ones of heavy quasi-particle, whose pairing drives the superconducting instability. These are the 