# Fractionalized Fermi liquids and the cuprate phase diagram

## TL;DR

This paper reviews a theoretical framework for cuprate superconductors based on fractionalized Fermi liquids (FL*), explaining the pseudogap phase, hole pockets, and transitions to other phases, supported by experimental and computational evidence.

## Contribution

It introduces the FL* theory with a layer construction and SU(2) gauge theory, explaining the pseudogap phase, Fermi arcs, and the FL*-FL transition without symmetry breaking.

## Key findings

- Magnetotransport measurements support the FL* hole pocket predictions.
- Monte Carlo simulations show hole pockets transforming into Fermi arcs.
- The theory describes a continuous FL*-FL transition driven by a critical charge liquid.

## Abstract

We review a theoretical framework for the cuprate superconductors, rooted in a fractionalized Fermi liquid (FL*) description of the intermediate-temperature pseudogap phase at low doping. The FL* theory predicted hole pockets each of fractional area $p/8$ at hole doping $p$, in contrast to the area $p/4$ in spin density wave theory. Magnetotransport measurements, including observation of the Yamaji angle, show clear evidence of hole pocket quasiparticles which can tunnel coherently between square lattice layers, and are consistent with the FL* description. The FL* phase of a single-band model is described using a layer construction with a pair of ancilla qubits on each site: the Ancilla Layer Model (ALM). Fluctuations are described by the SU(2) gauge theory of a background spin liquid with critical Dirac spinons. A Monte Carlo study of the thermal SU(2) gauge theory transforms the hole pockets into Fermi arcs in photoemission. One route to confinement of FL* upon lowering temperature yields a $d$-wave superconductor via a Kosterlitz-Thouless transition of $h/(2e)$ vortices, with nodal Bogoliubov quasiparticles featuring anisotropic velocities and vortices surrounded by charge order halos. Increasing doping from the FL* phase in the ALM drives a transition to a conventional Fermi liquid (FL) at large doping, passing through an intermediate strange metal regime. We formulate a theory of the FL*-FL metal-metal transition without a symmetry-breaking order parameter, using a critical quantum `charge' liquid of mobile electrons in the presence of disorder, developed via an extension of the Sachdev-Ye-Kitaev model to two spatial dimensions. At low temperatures, and across optimal and over doping, we address the regimes of extended non-Fermi liquid behavior by Griffiths effects near quantum phase transitions in disordered metals.