Thermodynamic properties of superconductors near magnetic quantum critical point*

I will present the results of the thermodynamic manifestations of the quantum criticality in multiband unconventional superconductors. As a guiding example I will consider the scenario of magnetic quantum critical point in the model that captures superconductivity coexistence with the spin-density wave. I will show that in situations when superconducting order parameter has incidental nodes at isolated points, quantum magnetic fluctuations lead to the renormalization of the relative T-linear slope of the London penetration depth. This leads to the nonmonotonic dependence of the penetration depth as a function of doping and the concomitant peak structure across the quantum critical point. The theoretical analysis will be corroborated by making a comparison of the results with the recent experimental data from the low-temperature thermodynamic measurements at optimal composition in BaFe$_2$(As$_{1-x}$P$_x$)$_2$