Calorimetric evidence for two phase transitions in Ba1-xKxFe2As2 with fermion pairing and quadrupling states

: Materials that break multiple symmetries allow the formation of four-fermion condensates above the superconducting critical temperature (Tc). Such states can be stabilized by phase fluctuations. Recently, a fermionic quadrupling condensate that breaks the Z2 time-reversal symmetry was reported in Ba1-xKxFe2As2. A phase transition to the new state of matter should be accompanied by a specific heat anomaly at the critical temperature where Z2 time-reversal symmetry is broken ([Formula: see text]). Here, we report on detecting two anomalies in the specific heat of Ba1-xKxFe2As2 at zero magnetic field. The anomaly at the higher temperature is accompanied by the appearance of a spontaneous Nernst effect, indicating the breakdown of Z2 symmetry. The second anomaly at the lower temperature coincides with the transition to a zero-resistance state, indicating the onset of superconductivity. Our data provide the first example of the appearance of a specific heat anomaly above the superconducting phase transition associated with the broken time-reversal symmetry due to the formation of the novel fermion order.