Microscopic Parameters from High-Resolution Specific Heat Measurements on Overdoped BaFe$_{2}$(As$_{1-x}$P$_{x}$)$_{2}$ Single Crystals

We investigate the electronic specific heat of overdoped BaFe$_{2}$(As$_{1-x}$P$_{x}$)$_{2}$ single crystals in the superconducting state using high-resolution nanocalorimetry. From the measurements, we extract the doping dependence of the condensation energy, superconducting gap $\Delta$, and related microscopic parameters. We find that the anomalous scaling of the specific heat jump $\Delta C \propto T_{\mathrm{c}}^3$, found in many iron-based superconductors, in this system originates from a $T_\mathrm{c}$-dependent ratio $\Delta/k_\mathrm{B}T_\mathrm{c}$ in combination with a doping-dependent density of states $N(\varepsilon_\mathrm{F})$. A clear enhancement is seen in the effective mass $m^{*}$ as the composition approaches the value that has been associated with a quantum critical point at optimum doping. However, a simultaneous increase in the superconducting carrier concentration $n_\mathrm{s}$ maintains the superfluid density, yielding an apparent penetration depth $\lambda$ that decreases with increasing $T_\mathrm{c}$ without sharp divergence at the quantum critical point. Uemura scaling indicates that $T_\mathrm{c}$ is governed by the Fermi temperature $T_\mathrm{F}$ for this multi-band system.