Thermodynamic properties of nodal superconductors close to a magnetic quantum critical point

In this work we study thermodynamic manifestations of the quantum criticality in multiband unconventional superconductors. As a guiding example consider scenario magnetic critical point model that captures superconductivity coexistence with spin-density wave. We show situations when superconducting order parameter has incidental nodes at isolated points, fluctuations lead to renormalization relative $T$-linear slope London penetration depth. This leads nonmonotonic dependence depth as function doping and concomitant peak structure across point. addition, determine contribution specific heat onset phase. Our theoretical analysis is corroborated by making comparison our results recent experimental data from low-temperature measurements optimal composition ${\mathrm{BaFe}}_{2}{({\mathrm{As}}_{1\ensuremath{-}x}{\mathrm{P}}_{x})}_{2}$.