Superconducting gap evolution in overdoped BaFe$_{2}$(As$_{1-x}$P$_x$)$_2$ single crystals through nanocalorimetry

We report on specific heat measurements on clean overdoped $mathrm{BaFe_{2}(As_{1-x}P_x)_2}$ single crystals performed with a high resolution membrane-based nanocalorimeter. A nonzero residual electronic specific heat coefficient at zero temperature $gamma_mathrm{r}={C/T}|_{T to 0}$ is seen for all doping compositions, indicating a considerable fraction of the Fermi surface ungapped or having very deep minima. The remaining superconducting electronic specific heat is analyzed through a two-band s-wave $alpha$ model in order to investigate the gap structure. Close to optimal doping we detect a single zero-temperature gap of $Delta_0 sim 5.3,mathrm{meV}$, corresponding to $Delta_0 / k_mathrm{B} T_mathrm{c} sim 2.2$. Increasing the phosphorus concentration $x$, the main gap reduces till a value of $Delta_0 sim 1.9,mathrm{meV}$ for $x = 0.55$ and a second weaker gap becomes evident. From the magnetic field effect on $gamma_mathrm{r}$, all samples however show similar behavior [$gamma_mathrm{r}(H) - gamma_mathrm{r}(H=0) propto H^n$, with $n$ between 0.6 and 0.7]. This indicates that, despite a considerable redistribution of the gap weights, the total degree of gap anisotropy does not change drastically with doping.

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.