Self-energy of a nodal fermion in a d-wave superconductor

TL;DR

This paper revisits the self-energy of nodal fermions in a 2D d-wave superconductor, revealing complex dependencies and divergences that challenge conventional beliefs, with implications for ARPES spectral features.

Contribution

It demonstrates that the self-energy depends on multiple variables and diverges at finite temperature, providing a more complete understanding of quasiparticle behavior in d-wave superconductors.

Findings

Self-energy depends on , T, and deviation from mass shell.

Divergence of second-order self-energy at finite T.

Non-monotonic ARPES spectral function with a kink.

Abstract

We re-consider the self-energy of a nodal (Dirac) fermion in a 2D d-wave superconductor. A conventional belief is that Im \Sigma (\omega, T) \sim max (\omega^3, T^3). We show that \Sigma (\omega, k, T) for k along the nodal direction is actually a complex function of \omega, T, and the deviation from the mass shell. In particular, the second-order self-energy diverges at a finite T when either \omega or k-k_F vanish. We show that the full summation of infinite diagrammatic series recovers a finite result for \Sigma, but the full ARPES spectral function is non-monotonic and has a kink whose location compared to the mass shell differs qualitatively for spin-and charge-mediated interactions.