Fractionalized Fermi liquids and cuprate phase diagram

TL;DR

The paper argues that cuprate phenomenology across the pseudogap, strange metal, and superconducting regimes can be understood from a fractionalized Fermi liquid FL* embedded in an Ancilla Layer Model with SU(2) gauge structure. It develops a detailed mean-field and gauge-theory description of FL* via layered spin liquids and spinon excitations, showing pocket areas of $p/8$ and coherent interlayer transport, reconciling photoemission and magnetotransport. It then connects the FL* to a strange-metal regime through SYK-inspired 2D Yukawa-SYK models, incorporating disorder and yielding universal transport and thermodynamic signatures including Planckian dissipation and Griffiths phases. The work further predicts confinement-driven transitions to $d$-wave superconductivity with anisotropic nodal velocities and vortex halos, and it discusses experimental tests such as Yamaji angles, Fermi arcs, and vortex halo imaging. Overall, the framework provides a unifying, anomaly-consistent route from pseudogap physics to unconventional superconductivity and non-Fermi liquid transport in cuprates.

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.

Figures (42)

• Figure 1: Cuprate phase diagram from Fig. 4 of Ref. SSwhere. (The only changes from the 2010 figure are that the pseudogap metal is now labeled FL*, dopings are denoted by $p$ rather than $x$, arrows have been removed, and section number annotations have been added; but all phase boundaries, crossovers, and critical points are the same.) The incipient FL*-FL transition at $p_c$Qi10SSMetlitskiPunk12YaHui-ancilla1 is that at $s_c$ in the normal state in Fig. \ref{['fig:flsfan']}; there is no transition at $p_c$ in the presence of superconductivity. The SDW transition at $p_{\rm sdw}$ is discussed in Section \ref{['sec:griffiths']} in the presence of disorder, where the "spin gap" region above becomes a Griffiths phase.
• Figure 2: Cuprate phase diagram from Ref. phase_diag. Annotations in blue have been added. We use a theory of a fractionalized Fermi liquid (FL*) of the pseudogap to connect to the other phases in the sections noted.
• Figure 3: Definitions of Fermi liquid (FL) and fractionalized Fermi liquid (FL*) for a general electronic lattice model. Here $\rho$ is the total density of electrons of both spins, and areas are measured as a fraction of Brillouin zone area. The mod 2 accounts for fully filled bands.
• Figure 4: A Kondo lattice of conduction electrons $c$ of density $p$ coupled to $S=1/2$ spins ${\bm S}_1$. All lattices are two-dimensional, although only one-dimensional projections are shown.
• Figure 5: Phase diagram of the Kondo lattice. The quoted areas are per spin. Neither phase has any symmetry breaking, but there is nevertheless a quantum phase transition (a Higgs transition in an emergent gauge theory) associated with Fermi volume change TSSSMV03TSSSMV04.