Unconventional spectral signature of T_c in a pure d-wave superconductor

In conventional superconductors, the phase transition into a zero-resistance and perfectly diamagnetic state is accompanied by a jump in the specific heat and the opening of a spectral gap¹. In the high-transition-temperature (high-T_c) cuprates, although the transport, magnetic and thermodynamic signatures of T_c have been known since the 1980s², the spectroscopic singularity associated with the transition remains unknown. Here we resolve this long-standing puzzle with a high-precision angle-resolved photoemission spectroscopy (ARPES) study on overdoped (Bi,Pb)₂Sr₂CaCu₂O_8+δ (Bi2212). We first probe the momentum-resolved electronic specific heat via spectroscopy and reproduce the specific heat peak at T_c, completing the missing link for a holistic description of superconductivity. Then, by studying the full momentum, energy and temperature evolution of the spectra, we reveal that this thermodynamic anomaly arises from the singular growth of in-gap spectral intensity across T_c. Furthermore, we observe that the temperature evolution of in-gap intensity is highly anisotropic in the momentum space, and the gap itself obeys both the d-wave functional form and particle-hole symmetry. These findings support the scenario that the superconducting transition is driven by phase fluctuations. They also serve as an anchor point for understanding the Fermi arc and pseudogap phenomena in underdoped cuprates.