Density of states and spectral function of a superconductor out of a quantum-critical metal

TL;DR

This paper investigates how superconductivity emerges from a quantum-critical metal, revealing that quasiparticle coherence can be lost depending on the nature of the quantum critical fluctuations, leading to non-BCS spectral features.

Contribution

It demonstrates that quasiparticle coherence in superconductors near a quantum critical point depends on the interaction's dynamical exponent, with breakdown occurring for certain models.

Findings

Quasiparticle coherence persists for interaction exponent γ<1/2.

Singular self-energy causes non-BCS density of states.

Quasiparticle peaks vanish for γ≥1/2.

Abstract

We analyze the validity of a quasiparticle description of a superconducting state at 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, should restore a coherent quasiparticle behavior. We argue that this does not necessarily hold as in some cases the fermionic self-energy remains singular slightly above the gap edge. This singularity gives rise to markedly non-BCS behavior of the density of states and to broadening and eventual vanishing of the quasiparticle peak in the spectral function. We analyze the set of quantum-critical models with an effective dynamical 4-fermion interaction, mediated by a gapless boson at a QCP, $V(\Omega) \propto 1/\Omega^\gamma$. 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 data.