The novel metallic states of the cuprates: Fermi liquids with topological order, and strange metals

Abstract

This article is based on a talk by S.S. at the Nambu Memorial Symposium at the University of Chicago. We review ideas on the nature of the metallic states of the hole-doped cuprate high temperature superconductors, with an emphasis on the connections between the Luttinger theorem for the size of the Fermi surface, topological quantum field theories (TQFTs), and critical theories involving changes in the size of the Fermi surface. We begin with the derivation of the Luttinger theorem for a Fermi liquid, using momentum balance during a process of flux-insertion in a lattice electronic model with toroidal boundary conditions. We then review the TQFT of the Z2 spin liquid, and demonstrate its compatibility with the toroidal momentum balance argument. This discussion leads naturally to a simple construction of `topological' Fermi liquid states: the fractionalized Fermi liquid (FL*) and the algebraic charge liquid (ACL). We present arguments for a description of the pseudogap metal of the cuprates using Z2-FL* or Z2-ACL states with Ising-nematic order. These pseudogap metal states are also described as Higgs phases of a SU(2) gauge theory. The Higgs field represents local antiferromagnetism, but the Higgs-condensed phase does not have long-range antiferromagnetic order: the magnitude of the Higgs field determines the pseudogap, the reconstruction of the Fermi surface, and the Ising-nematic order. Finally, we discuss the route to the large Fermi surface Fermi liquid via the critical point where the Higgs condensate and Ising nematic order vanish, and the application of Higgs criticality to the strange metal.

34 pages, 11 figures; (v2) 35 pages. Expanded discussion of experiments and added citation to arXiv:1606.07813; (v4+5) Same as published version, but updated terminology on topological phases to align with general usage

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Cited by in corpus (37)

• Topological order, emergent gauge fields, and Fermi surface reconstruction
• String patterns in the doped Hubbard model
• Three dimensional collective charge excitations in electron-doped cuprate superconductors
• Confinement transition of ${\mathbb{Z}}_2$ gauge theories coupled to massless fermions: emergent QCD${}_3$ and $SO(5)$ symmetry
• Parton theory of magnetic polarons: Mesonic resonances and signatures in dynamics
• Parton theory of ARPES spectra in anti-ferromagnetic Mott insulators
• A critical strange metal from fluctuating gauge fields in a solvable random model
• Visualizing Strange Metallic Correlations in the 2D Fermi-Hubbard Model with AI
• Confinement and Mott transitions of dynamical charges in 1D lattice gauge theories
• SU(2) gauge theory of the pseudogap phase in the two-dimensional Hubbard model
• Thermal and electrical transport in metals and superconductors across antiferromagnetic and topological quantum transitions
• Insulators and metals with topological order and discrete symmetry breaking
• Two dimensional spin liquids with ${\mathbb{Z}}_2$ topological order in an array of quantum wires
• Rotational Resonances and Regge Trajectories in Lightly Doped Antiferromagnets
• Moiré phonons and impact of electronic symmetry breaking in twisted trilayer graphene
• Spin Liquids and Pseudogap Metals in $SU(4)$ Hubbard Model in Moiré Superlattice
• Exact solution of a two-species quantum dimer model for pseudogap metals
• $Z_2$ fractionalized phases of a solvable, disordered, $t$-$J$ model
• Doping-dependent competition between superconductivity and polycrystalline charge density waves
• Confinement in 1+1D ${\mathbb{Z}}_2$ Lattice Gauge Theories at Finite Temperature
• Charge-Density Waves vs. Superconductivity: Some Results and Future Perspectives
• Density response and collective modes of semi-holographic non-Fermi liquids
• Zero sound and higher-form symmetries in compressible holographic phases
• Exact Hole-induced Resonating-Valence-Bond Ground State in Certain $U=\infty$ Hubbard Models
• Electron spectral functions in a quantum dimer model for topological metals
• Topological nature of Hubbard bands in strongly correlated systems
• Feshbach hypothesis of high-Tc superconductivity in cuprates
• Bound states of fractionalized excitations in a modulated Kitaev spin liquid
• Suppression of Hall number due to charge density wave order in high-$T_c$ cuprates
• Single-Particle Dispersion and Density of States of the Half-Filled 2D Hubbard Model
• A slave boson description of pseudogap metals in t-J models
• Geometric orthogonal metals: Hidden antiferromagnetism and pseudogap from fluctuating stripes
• Signatures of correlated magnetic phases in the local two-particle density matrix
• Solvable lattice models for metals with Z2 topological order
• Increased critical temperature $T_c$ in the ideal anisotropic boson gas
• Spin susceptibility in a pseudogap state with fluctuating spiral magnetic order
• Visualizing spinon Fermi surfaces with time-dependent spectroscopy