Multi-Method Specific Heat Investigation of the Overdoped High-Tc Superconductor, BaFe$_{\mathrm{2}}$(As$_{\mathrm{1-x}}$P$_{\mathrm{x}})_{\mathrm{2}}$

We examine the specific heat of the iron-based high-temperature superconductor, BaFe$_{\mathrm{2}}$(As$_{\mathrm{1-x}}$P$_{\mathrm{x}})_{\mathrm{2}}$ for 0.44$\le $x$\le $0.60 using three distinct methods: zero-magnetic-field analysis of the jump in specific heat at T$_{\mathrm{c}}$, zero-magnetic-field determination of the electronic specific heat in the T$=$0 limit, and, most importantly, high-magnetic-field measurement of the electronic specific heat in which we suppress superconductivity to reveal the normal state specific heat [1]. We report the coupling strength parameter $\alpha_{\mathrm{c}}=\Delta $C/($\gamma _{\mathrm{n}}$T$_{\mathrm{c}})$ as a function of doping. We also observe a finite, zero-temperature specific heat, which has also been reported in Ba(Fe$_{\mathrm{1-x}}$Co$_{\mathrm{x}})_{\mathrm{2}}$As$_{\mathrm{2}}$ [2] and the cuprates [3]. By comparing the three methods, we are able to deduce a consistent treatment of specific heat measurements in this iron-based high-temperature superconductor. The data establish that mass enhancement occurs in multiple bands as optimal doping is approached and, furthermore, $\alpha_{\mathrm{c}}$ deviates from the expected BCS value. [1] Moir, C.M. et. al. arXiv:1608.07510 (2016) [2] Gang, MU, et. al. Chinese Phys. Lett. 27 037402 (2010) [3] Brooks, J.S. and J. R. Schieffer, editors. Handbook of High-Temperature Superconductivity, (2007).