Direct observation of the Lindhard continuum using Resonant Inelastic X-ray Scattering

The most elementary low-energy excitations of a Fermi liquid are particle-hole excitations obtained by scattering a quasiparticle across the Fermi surface, which generally form a continuous, bounded region in energy and momentum space, known as the Lindhard continuum. Despite the ubiquitous nature of the continuum, direct spectroscopic signatures of the intraband excitations involved in it have remained elusive. In this talk, I will discuss our recent observation and analysis of a low-energy, linearly dispersing feature in the Resonant Inelastic X-ray Scattering (RIXS) spectrum of MgB₂ and its connection to the continuum of particle-hole excitations in this material. Our detailed simulations of the experimental spectrum overlap significantly with the non-interacting Lindhard function, and the latter is found to be dominated by excitations of intra-band origin. Our analysis conclusively demonstrates that the low-energy feature observed in the RIXS spectrum of MgB₂ directly maps out the Lindhard continuum in this material, constituting the first direct spectroscopic observation of the continuum. Further, our results establish RIXS as a powerful orbital-selective and momentum-sensitive probe of elementary charge dynamics, across families of weakly and strongly correlated materials.