Quantum Criticality of Multiband Polar Metals*

Quantum criticality in metallic systems leads to a variety of exotic behaviors, that sensitively depend on the type of the transition. The case of a polar transition in a metal, structurally identical to a ferroelectric transition in an insulator, has received attention recently due to the discovery of a number of metallic compounds where a polar order exists.

We show that quantum criticality of multiband polar metals is of particular interest, as a strong coupling of the charge carriers to the critical mode can be realized near the band crossings in momentum space. We provide a comprehensive classification of the possible emerging quantum critical behaviors and find evidence for strong interaction effects and, in some cases, non-Fermi liquid physics. The critical properties are found to depend on the type of band crossing as well as dimensionality. Experiments, that can allow to probe the emergent behavior, and implications for existing materials are discussed.