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. Inspired by the success in explaining classic $115$-series heavy fermion superconductors, we expect the present theory can be applied to understand other heavy fermion superconductors like CeCu$_{2}$Si$_{2}$ and more generic multi-band superconductors.'
author:
- Yin Zhong
- Lan Zhang
- Can Shao
- 'Hong-Gang Luo'
title: Superfluid response in heavy fermion superconductors
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Introduction {#sec1}
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Superfluid density or London penetration depth measurement is a fundamental experimental tool to detect low-temperature superconducting quasi-particle excitation in highly entangled unconventional pairing ground-state.[@Tinkham; @Xiang; @Poole] The low-temperature behavior of such quantity has provided invaluable information on the pairing symmetry for high-$T_{c}$ cuprate, iron pnictide and heavy fermion superconductors.[@Hardy1993; @Kim2003; @Prozorov; @Ormeno2002; @Ozcan2003; @Chia2003; @Hashimoto2013; @Truncik2013; @Shu2014; @Kim2015]

In the field of heavy fermion compound, power-law temperature-dependence of superfluid density has been widely observed in the classic quasi-two-dimensional heavy fermion superconductor CeCoIn$_{5}$ with remarkably high $T_{c}=2.3\mathrm{K}$,[@Monthoux2001; @Ormeno2002; @Ozcan2003; @Chia2003; @Hashimoto2013; @Truncik2013; @Shu2014] although its detailed power-law behavior is still controversial due to proximity to possible magnetic quantum critical point.[@Ormeno2002; @Ozcan2003; 