Fig. 1: Split transitions in hole overdoped Ba_1−xK_xFe₂As₂.

Temperature dependence of the zero-field specific heat ΔC_el/T and the static magnetic susceptibility measured in B∥ab = 0.5 mT. e shows the data for the sample from ref. ¹² with the quartic metal phase and doping level x = 0.77. T_c is defined by zero resistance and \({T}_{{{{{{{{\rm{c}}}}}}}}}^{{{{{{{{\rm{Z2}}}}}}}}}\) is shown according to the onset of the spontaneous magnetic fields and spontaneous Nernst effect. A distinct specific heat anomaly at \({T}_{{{{{{{{\rm{c}}}}}}}}}^{{{{{{{{\rm{Z2}}}}}}}}}\) was not resolved within error bars of the measurements. a–d, f show the data for the samples studied in this work. a, f correspond to reference samples with doping levels x ≈ 0.69 and x ≈ 0.90, respectively. These two samples have a doping level outside the range of doping, where BTRS occurs^21,24 show the conventional picture, where the onset of the specific heat is consistent with the onset of a superconducting response in the susceptibility. This behavior is indistinguishable from the standard mean-field behavior of a superconductor with a single-phase transition at T_c. b–d are for the samples with BTRS state and doping level x ≈ 0.75. These samples show two anomalies in the specific heat. The anomaly at a higher temperature, highlighted by black arrows, appears at the Z₂ transition (see Fig. 2).