date, there is still no consensus on the true mechanism of such unconventional pairing and we are forced to reconsider this issue with more phenomenological approach.[@Coleman]

Theoretically, in both RVB or spin-fluctuation-exchange theory, the superconducting pairing is induced by certain effective antiferromagnetic interaction. The main difference is that the former emphasizes local real-space correlation while the latter one is focused on dynamic exchange of energy/momentum, i.e. the collective antiferromagnetic fluctuation. In practice, since the observed pairing structure in heavy fermion superconductor has strong momentum-dependent behavior, one may expect that the driving force of pairing is the space-dependent part of effective pairing interaction rather than its time/energy part. In the other words, we may imagine a real-space pairing interaction and if we take the magnetic (fluctuation) nature of interaction into account, we will arrive at the following phenomenological local magnetic exchange interaction[@Hu2012] $$\begin{aligned}
H_{int}=\sum_{ij}J_{ij}\vec{S}_{i}^{f}\cdot\vec{S}_{j}^{f}.\nonumber\end{aligned}$$ Here, the spin density operator denotes the spin degree of freedom of local f-electron , which should result from the existing RKKY interaction. Furthermore, if only nearest-neighbor coupling is involved, this term naturally evolves into the Heisenberg term in Kondo-Heisenberg model. That is to say that the Kondo-Heisenberg model itself has already included the basic element of 