Quantum Critical Polar Metals

Recent studies show that ferroelectric materials can be tuned to quantum criticality. Doping these systems gives rise to quantum critical polar metals, where structural phase transitions formally replace ferroelectric ones. This raises the following key questions: how does the presence of itinerant carriers alter the nature of the transition and what is the interaction between the electrons in this novel quantum critical fluid? Motivated by these considerations, we develop an analytic model for a Fermi sea of conduction electrons coupled to a critical ferroelectric mode, where screening is taken into account. Using diagrammatic methods we consider the suppression of the transition in the system with increasing doping, and develop a description of the dielectric properties of the quantum critical polar metal. Experimental implications for doped strontium titanate and similar systems are discussed.