Dielectric anomalies and interactions in the three-dimensional quadratic band touching Luttinger semimetal Pr 2 Ir 2 O 7 .

Dirac and Weyl semimetals with linearly crossing bands are the focus of much recent interest in condensed matter physics. Although they host fascinating phenomena, their physics can be understood in terms of weakly interacting electrons. In contrast, more than 40 years ago, Abrikosov pointed out that quadratic band touchings are generically strongly interacting. We have performed terahertz spectroscopy on the films of the conducting pyrochlore Pr2 Ir2 O7 , which has been shown to host a quadratic band touching. A dielectric constant as large as [Formula: see text] is observed at low temperatures. In such systems, the dielectric constant is a measure of the relative scale of interactions, which are therefore in our material almost two orders of magnitude larger than the kinetic energy. Despite this, the scattering rate exhibits a T 2 dependence, which shows that for finite doping a Fermi liquid state survives-however, with a scattering rate close to the maximal value allowed.