Thermodynamic signatures of an antiferromagnetic quantum critical point inside a superconducting dome

Abstract

Recent experiments in unconventional superconductors, and in particular iron-based materials, have reported evidence of an antiferromagnetic quantum critical point (AFM-QCP) emerging inside the superconducting dome of the phase diagram. Fluctuations associated with such an AFM-QCP are expected to promote unusual temperature dependencies of thermodynamic quantities. Here, we compute the $T$ dependence of the specific heat $C(T)$ deep inside a fully gapped $s^{+-}$ superconducting state as the AFM-QCP is approached. We find that, at the AFM-QCP, the specific heat $C(T)$ vanishes quadratically with temperature, as opposed to the typical exponential suppression seen in fully-gapped BCS superconductors. This robust result is due to a non-analytic contribution to the free-energy arising from the general form of the bosonic (AFM) propagator in the SC state. Away from the AFM-QCP, as temperature is lowered, $C(T)$ shows a crossover from a $T^2$ behavior to an exponential behavior, with the crossover temperature scale set by the value of the superconducting gap and the distance to the QCP. We argue that these features in the specific heat can be used to unambiguously determine the existence of AFM-QCPs inside the superconducting domes of iron-based and other fully gapped unconventional superconductors.

arXiv comment10 pages, 5 figures, new Section V included

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• Thermodynamic properties of nodal superconductors close to a magnetic quantum critical point
• Transport anomalies in multiband superconductors near quantum critical point
• Interacting fermions in narrow-gap semiconductors with band inversion
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• Reaching Quantum Critical Point by Adding Non-magnetic Disorder in Single Crystals of Superconductor $({\text{Ca}}_x{\text{Sr}}_{1-x}{)}_3{\text{Rh}}_4{\text{Sn}}_{13}$