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Theoretically, materials that break multiple symmetries allow, under certainconditions, the formation of four-fermion condensates above the superconductingcritical temperature. Such states can be stabilized by phase fluctuations.Recently a fermionic quadrupling condensate that breaks the $Z_2$ time-reversalsymmetry was reported in Ba$_{\rm 1-x}$K$_{\rm x}$Fe$_{2}$As$_{2}$ [V. Grinenkoet al., Nat. Phys. 17, 1254 (2021)]. Evidence for the new state of matter comesfrom muon-spin rotation, transport, thermoelectric, and ultrasound experiments.Observing a specific heat anomaly is a very important signature of a transitionto a new state of matter. However, a fluctuation-induced specific heatsingularity is usually very challenging to resolve from a background of othercontributions. Here, we report on detecting two anomalies in the specific heatof Ba$_{\rm 1-x}$K$_{\rm x}$Fe$_{2}$As$_{2}$ at zero magnetic field. Theanomaly at the higher temperature is accompanied by the appearance of aspontaneous Nernst effect, indicating broken time-reversal ($Z_2$) symmetry.The second anomaly at the lower temperature coincides with the transition to azero resistance state, indicating superconductivity breaking the $U(1)$ gaugesymmetry. Our data provide calorimetric evidence for the $Z_2$ phase formationabove the superconducting phase transition.

Calorimetric evidence for two phase transitions in Ba$_{\rm 1-x}$K$_{\rm x}$Fe$_{2}$As$_{2}$ with fermion pairing and quadrupling states