We analyze the validity of a quasiparticle description of a superconducting state above a metallic quantum-critical point (QCP). A normal state at a QCP is a non-Fermi liquid with no coherent quasiparticles. A superconducting order gaps out low-energy excitations, except for a sliver of states for non-$s$-wave gap symmetry, and at a first glance, restores coherent quasiparticle behavior. We argue that this does not necessarily hold as the fermionic self-energy may remain singular above the gap edge. This singularity gives rise to markedly non-BCS behavior of the density of states and to the appearance of a nondispersing mode at the gap edge in the spectral function. We analyze the set of quantum-critical models with an effective dynamical four-fermion interaction $V(\mathrm{\Omega })\propto 1/{\mathrm{\Omega }}^{\gamma }$, where $\mathrm{\Omega }$ is a frequency of a boson, which mediates the interaction. We show that coherent quasiparticle behavior in a superconducting state holds for $\gamma <1/2$, but breaks down for larger $\gamma$. We discuss signatures of quasiparticle breakdown and compare our results with the photoemission data for Bi2201 and Bi2212.

• Received 30 January 2023
• Accepted 25 July 2023

DOI:https://doi.org/10.1103/PhysRevLett.131.086502