A model of $d$-wave superconductivity, antiferromagnetism, and charge order on the square lattice

Abstract

Early studies proposed a connection between cuprate superconductivity and fractionalized spin liquid states. But the low temperature phase diagram is dominated by states without fractionalization, with a competition between superconductivity and charge-ordered states which break translational symmetry. Our theory uncovers novel features associated with a particular spin-liquid presumed to underlie the pseudogap metal, and shows that it has multiple nearly-degenerate instabilities to confinement of fractionalized excitations, leading to antiferromagnetism, $d$-wave superconductivity, and/or charge order. Our theory provides routes to resolving a number of open puzzles on the cuprate phase diagram. The spin liquid is described by a SU(2) gauge theory of $N_f=2$ massless fundamental Dirac fermions, has an emergent SO(5)${}_f$ global symmetry, and is presumed to confine at low energies to the Néel state. At non-zero doping (or smaller Hubbard repulsion at half-filling) we argue that confinement occurs via the Higgs condensation of bosonic chargons carrying fundamental SU(2) gauge charges moving in $\pi$ flux. At half-filling, the low energy Higgs sector has $N_b=2$ relativistic bosons with a possible emergent SO(5)${}_b$ global symmetry describing rotations between a $d$-wave superconductor, period-2 charge stripes, and the time-reversal breaking `$d$-density wave' state. We propose a deconfined quantum critical point between a confining state which breaks SO(5)${}_f$ and a confining state which breaks SO(5)${}_b$. The pattern of symmetry breaking within both SO(5)s is determined by terms likely irrelevant at the critical point, which can be chosen to obtain a transition between Néel order and $d$-wave superconductivity. A similar theory applies at non-zero doping and large $U$, with longer-range couplings of the chargons leading to charge order with longer periods.

10+9 pages, 10+5 figures; v4 Added Ya-Hui Zhang as co-author; v6 added grant acknowledgement to Moore Foundation

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Cited by in corpus (24)

• Charge Transfer and Zhang-Rice Singlet Bands in the Nickelate Superconductor $\mathrm{L}{\mathrm{a}}_3\mathrm{N}{\mathrm{i}}_2{\mathrm{O}}_7$ under Pressure
• Evidence of Dirac Quantum Spin Liquid in YbZn2GaO5
• Phases of (2+1)D SO(5) non-linear sigma model with a topological term on a sphere: multicritical point and disorder phase
• Stable computation of entanglement entropy for 2D interacting fermion systems
• Spin density wave, Fermi liquid, and fractionalized phases in a theory of antiferromagnetic metals using paramagnons and bosonic spinons
• Strange metals and black holes: insights from the Sachdev-Ye-Kitaev model
• The foot, the fan, and the cuprate phase diagram: Fermi-volume-changing quantum phase transitions
• Emergence of nodal Bogoliubov quasiparticles across the transition from the pseudogap metal to the d-wave superconductor
• Equilibration of Topological Defects Near the Deconfined Quantum Multicritical Point
• Deconfined Quantum Critical Point: A Review of Progress
• Deconfined quantum criticality of nodal $d$-wave superconductivity, Néel order, and charge order on the square lattice at half-filling
• Feshbach hypothesis of high-Tc superconductivity in cuprates
• Quantum oscillations in the hole-doped cuprates and the confinement of spinons
• Topological physics in quantum critical systems
• Vortex structure in a $d$-wave superconductor obtained by a confinement transition from the pseudogap metal
• Fractionalized Fermi liquids and the cuprate phase diagram
• Canted magnetism and ${\mathbb{Z}}_2$ fractionalization in metallic states of the Lieb lattice Hubbard model near quarter filling
• Charge modulation in the background of depleted superconductivity inside vortices
• Thermopower across Fermi-volume-changing quantum phase transitions without translational symmetry breaking
• Probing the pseudogap and beyond: Examining single-particle properties of the hole- and electron-doped Hubbard model
• Strain-induced structural change and nearly-commensurate diffuse scattering in the model high-temperature superconductor HgBa${}_2$CuO${}_{4+\delta }$
• Emergent Chiral Metal near a Kondo Breakdown Quantum Phase Transition
• Spin liquid phase in the Hubbard model: Luttinger-Ward analysis of the slave-rotor formalism
• Pseudogap in electron-doped cuprates: thermal precursor to magnetism