Superconductivity mediated by nematic fluctuations -- the dispersion of collective modes

TL;DR

This paper investigates the collective mode spectrum in superconductors where pairing is driven by nematic fluctuations, revealing unconventional dispersions and spectral features distinct from traditional BCS superconductors.

Contribution

It derives the pair susceptibility at finite momentum and frequency in nematic-fluctuation-mediated superconductors, highlighting unique collective mode dispersions and spectral properties.

Findings

Spectral function shows distinct pole structures in transverse and longitudinal channels.

Collective modes exhibit highly unconventional dispersion relations.

The pair susceptibility differs qualitatively from that of a conventional BCS superconductor.

Abstract

We analyze the spectrum of collective modes in a superconductor in which pairing is mediated by long-range nematic fluctuations. Previous experimental and theoretical studies have found that the superconducting gap in such a system is highly anisotropic and, at any finite $T<T_c$, vanishes on four arcs of the Fermi surface, even when the pairing symmetry is $s$ wave ($s^{+-}$ between hole and electron pockets). We derive the expression for the pair susceptibility $\chi(\mathbf{q},\Omega)$ at finite momentum $\mathbf{q}$ and frequency $\Omega$ deep in the superconducting phase. We analyze the spectral function, $\operatorname{Im}\chi(\mathbf{q},\Omega)$, and its pole structure in the transverse (phase) and longitudinal (amplitude) channels, and compare the results with those of a conventional $s$-wave superconductor. We find that the analytic structure of the pair susceptibility in both channels is qualitatively distinct from that in a BCS superconductor. This gives rise to a highly unconventional dispersion of phase and amplitude collective modes.