Unified non-Fermi liquid and superconductivity in a model of strongly-correlated systems

Abstract

We study a model of strongly-correlated systems that incorporates phases such as Fermi liquids, non-Fermi liquids, and superconductivity, in addition to potential intertwined orders. The model describes Fermi surfaces of spinful electron gas or electron liquid coupled to bosons via an intermediate gauge field. Effectively, the coupling imposes constraints and interactions between the fermion spin and the local boson density. This grants the bosons the meaning as the Schwinger boson of the magnetic order and allows us to probe a larger phase space, rather than around the quantum critical point. We design the initial model so that after the boson and gauge fields are integrated out exactly, the resulting fermion-only effective theory only consists of several local interactions, allowing controlled weak-coupling interpretation for certain parameter regions. Consequently, we find a non-Fermi liquid whose degrees of freedom in the effective theory take the form of an \emph{emergent} Fermi surface that has a different Luttinger volume from the original fermions, therefore explicitly violates the Luttinger theorem. Further, this allows a $d$-wave superconducting instability if the effective interacting induced by boson coupling is in the relevant pairing channel. When the emergent Fermi surface undergoes a Lifshitz transition, the carrier type changes. In addition, we attribute the Mott insulating behavior in the strong coupling limit to the loss of emergent Fermi surface and argue the possibility of coexisting magnetic order. Our effective theory also suggests the possibility of charge density waves as a consequence of \emph{effective} strong repulsion and is independent of the Fermi-surface-nesting scenario. We discuss the possible optimal conditions for higher superconducting transition temperature and potential relevances and implications for realistic materials.