Critical Quadrupole Fluctuations and Collective Modes in Iron Pnictide Superconductors

The multiband nature of iron pnictides gives rise to a rich temperature-doping phase diagram of competing orders and a plethora of collective phenomena. At low dopings, the tetragonal-to-orthorhombic structural transition is closely followed by a spin density wave transition both being in close proximity to the superconducting phase. A key question is the nature of high-$T_c$ superconductivity and its relation to orbital ordering and magnetism. Here we study the NaFe$_{1-x}$Co$_{x}$As superconductor using polarization-resolved Raman spectroscopy. The Raman susceptibility displays critical enhancement of non-symmetric charge fluctuations across the entire phase diagram which are precursors to a $d$-wave Pomeranchuk instability at temperature $\theta(\mbox{x})$. The charge fluctuations are interpreted in terms of quadrupole inter-orbital excitations in which the electron and hole Fermi surfaces breathe in-phase. Below $T_c$, the critical fluctuations acquire coherence and undergo a metamorphosis into a coherent ingap mode of extraordinary strength.