Critical Charge Fluctuations and Ingap Collective Modes in the Superconducting State of the NaFe$_{\mathrm{1-x}}$Co$_{\mathrm{x}}$As Iron Pnictide Superconductor*

We use polarization-resolved Raman spectroscopy to study the Raman susceptibility ($\chi (\omega $,T,x)) of the x-T phase diagram of NaFe$_{\mathrm{1-x}}$Co$_{\mathrm{x}}$As [1]. Above the structural T$_{\mathrm{S}}$(x) and the superconducting T$_{\mathrm{c}}$(x) transition, $\chi (\omega $,T,x) is dominated by a low-frequency quasielastic peak in B$_{\mathrm{2g}}$ symmetry displaying critical behavior across the entire phase diagram. Below T$_{\mathrm{c}}$(x), sharp ingap modes emerge for x$\ge $0.0165 in A$_{\mathrm{1g}}$ ($\approx $65 cm$^{-1})$ and B$_{\mathrm{2g}}$ ($\approx $25 and $\approx $55 cm$^{-1})$ symmetry. The critical charge fluctuations are interpreted in terms of plasma waves of quadrupole excitations which below T$_{\mathrm{c}}$(x) undergo a metamorphosis into the ingap modes. The A$_{\mathrm{1g}}$ mode is a particle-hole (p-h) charge exciton consistent with a non-conventional s$+$- superconducting groundstate. The minor B$_{\mathrm{2g}}$ mode is a Bardasis-Schrieffer Cooper pair exciton of d-wave symmetry which exists only in a narrow doping window of density wave and superconductivity coexistence. The major B$_{\mathrm{2g}}$ mode is a bound state of d$+$- p-h plasma oscillations. \\[4pt] [1] V. K. Thorsm{\o}lle \textit{et al.} arXiv:1410.6456v1.