Fractionalized Fermi liquid with bosonic chargons as a candidate for the pseudogap metal (1607.05727v2)

Abstract: Doping a Mott-insulating $\mathbb{Z}_2$ spin liquid can lead to a fractionalized Fermi liquid (FL*). Such a phase has several favorable features that make it a candidate for the pseudogap metal for the underdoped cuprates. We focus on a particular, simple $\mathbb{Z}_2$-FL* state which can undergo a confinement transition to a spatially uniform superconductor which is smoothly connected to the plain vanilla' BCS superconductor with $d$-wave pairing. Such a transition occurs by the condensation of bosonic particles carrying $+e$ charge but no spin (chargons'). We show that modifying the dispersion of the bosonic chargons can lead to confinement transitions with charge density waves and pair density waves at the same wave-vector $\mathbf{K}$, co-existing with $d$-wave superconductivity. We also compute the evolution of the Hall number in the normal state during the transition from the plain vanilla FL* state to a Fermi liquid, and argue, following Coleman, Marston, and Schofield [Phys. Rev. B 72, 245111 (2005)], that it exhibits a discontinuous jump near optimal doping. We note the distinction between these results and those obtained from models of the pseudogap with fermionic chargons.