Unusual Friedel and RKKY responses in 3D quadratic band-touching Luttinger semimetals*

We study the response of Luttinger semimetals, such as alpha-Sn, HgSe, HgTe, YPtBi and Pr₂Ir₂O₇, to charge and magnetic impurities. In these materials the strong spin-orbit coupling and quadratic band-touching lead to unusual Friedel and Ruderman-Kittel-Kasuya-Yoshida (RKKY) oscillations, as well as an asymmetry in the response upon electron or hole doping. We also examine the magnetic Pauli and Landau susceptibilities, which differ from those of regular metals. These results motivate the study of Kondo physics in Luttinger semimetals, where novel quantum phases can arise due to spin-orbit coupling.