Lattice Dynamics Signatures of Competing Orders in Unconventional Superconductors

Introduction Unconventional superconductivity typically refers to a superconducting state that stems from an effective attractive interaction between electronic quasiparticles, which is not the canonical electron-phonon coupling (EPC) [1]. The latter has been the key ingredient in unveiling the Cooper pairing mechanism on which builds the conventional theory of superconductivity (or theory of conventional superconductivity) originally proposed by Bardeen, Cooper, and Schrieffer [2]. The large variety of unconventional superconducting materials indicates that there is probably no unified theory of unconventional superconductivity that could account for all phenomena encountered in these materials. Nevertheless, it appears empirically that unconventional superconductivity often emerges in the neighborhood of closely degenerate electronic phases, which coexist, sometimes compete, or are even intertwined with the superconducting state [3, 4]. Critical fluctuations associated with these other electronic phases are often suspected to play a decisive role in unconventional superconducting pairing, which has in turn motivated the development of experimental tools allowing us to probe materials of interest at energies and momenta matched to their intrinsic collective responses. As such, even though the EPC does not appear to be the primary driver of unconventional superconductivity, the coupling of electronic to lattice degrees of freedom has proven to be a sensitive probe of competing orders. Renormalization of the phonon spectra across electronic phase transitions is a particularly well-suited approach for these investigations. It has recently benefited a lot from the development of inelastic X-ray scattering (IXS) [5], which enables in particular the use of high pressures (in the tens of GPa range) as a “clean” way to drive a system across phase transitions. In this short topical review, we illustrate this by reporting three recent cases in which phonon spectroscopy has been particularly insightful in addressing the physics of competing orders in unconventional superconductors, namely the high-temperature superconducting cuprates, Fe-based superconductors, and their Ni-based cousins.