Fractionalized Fermi liquid with bosonic chargons as a candidate for the pseudogap metal

TL;DR

This paper explores a fractionalized Fermi liquid state with bosonic chargons as a model for the pseudogap phase in underdoped cuprates, analyzing confinement transitions, density waves, and Hall number evolution.

Contribution

It introduces a simple $ ext{Z}_2$-FL* model with bosonic chargons that can undergo confinement transitions to superconductivity and density waves, providing new insights into pseudogap phenomena.

Findings

Bosonic chargon dispersion affects confinement transitions.

Charge and pair density waves can coexist with $d$-wave superconductivity.

Hall number exhibits a discontinuous jump near optimal doping.

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.