Competing orders in a magnetic field: spin and charge order in the cuprate superconductors

Abstract

We describe two-dimensional quantum spin fluctuations in a superconducting Abrikosov flux lattice induced by a magnetic field applied to a doped Mott insulator. Complete numerical solutions of a self-consistent large N theory provide detailed information on the phase diagram and on the spatial structure of the dynamic spin spectrum. Our results apply to phases with and without long-range spin density wave order and to the magnetic quantum critical point separating these phases. We discuss the relationship of our results to a number of recent neutron scattering measurements on the cuprate superconductors in the presence of an applied field. We compute the pinning of static charge order by the vortex cores in the `spin gap' phase where the spin order remains dynamically fluctuating, and argue that these results apply to recent scanning tunnelling microscopy (STM) measurements. We show that with a single typical set of values for the coupling constants, our model describes the field dependence of the elastic neutron scattering intensities, the absence of satellite Bragg peaks associated with the vortex lattice in existing neutron scattering observations, and the spatial extent of charge order in STM observations. We mention implications of our theory for NMR experiments. We also present a theoretical discussion of more exotic states that can be built out of the spin and charge order parameters, including spin nematics and phases with `exciton fractionalization'.

36 pages, 33 figures; for a popular introduction, see http://onsager.physics.yale.edu/superflow.html; (v2) Added reference to new work of Chen and Ting; (v3) reorganized presentation for improved clarity, and added new appendix on microscopic origin; (v4) final published version with minor changes

References in corpus (70)

• Electronic Liquid Crystal Phases of a Doped Mott Insulator
• A Four-Unit-Cell Periodic Pattern of Quasiparticle States Surrounding Vortex Cores in Bi2Sr2CaCu2O8+d
• Z_2 Gauge Theory of Electron Fractionalization in Strongly Correlated Systems
• The doping dependence of T* - what is the real high-Tc phase diagram?
• Antiferromagnetic Order Induced by an Applied Magnetic Field in a High-Temperature Superconductor
• Quantum Criticality: competing ground states in low dimensions
• Stripe phases in high-temperature superconductors
• Spins in the Vortices of a High Temperature Superconductor
• Superconducting Vortex with Antiferromagnetic Core
• Spin ordering quantum transitions of superconductors in a magnetic field
• Universal quantum critical dynamics of two-dimensional antiferromagnets
• The Spin Excitation Spectrum in Superconducting $\mathbf{YB}{\mathbf{a}}_2\mathbf{C}{\mathbf{u}}_3{\mathbf{O}}_{6.85}$
• Neutron Scattering Study of Spin Density Wave Order in the Superconducting State of Excess-Oxygen-Doped La2CuO4+y
• Toward a Unified Magnetic Phase Diagram of the Cuprate Superconductors
• The Phase Diagrams of F=2 Spinor Bose Condensates
• Spinor Bosonic Atoms in Optical Lattices: Symmetry Breaking and Fractionalization
• Observation of New Incommensurate Magnetic Correlations at the Lower Critical Concentration for Superconductivity (x=0.05) in La(2-x)Sr(x)CuO4
• Landau Theory of Stripe Phases in Cuprates and Nickelates
• Theory of the Resonant Neutron Scattering of High $T_c$ Superconductors
• Charge order, superconductivity, and a global phase diagram of doped antiferromagnets
• Quantum Impurity in a Nearly Critical Two Dimensional Antiferromagnet
• Spin-fermion model near the quantum critical point: one-loop renormalization group results
• Plaquette Boson-Fermion Model of Cuprates
• Superconductivity-Induced Anomalies in the Spin Excitation Spectra of Underdoped YBa_2 Cu_3 O_{6+x}
• Universal Magnetic Properties of $L{a}_{2-\delta }S{r}_{\delta }Cu{O}_4$ at Intermediate Temperatures
• Competing orders and quantum criticality in doped antiferromagnets
• Enhancement of long-range magnetic order by magnetic field in superconducting La2CuO(4+y)
• Anomalous isotopic effect near the charge-ordering quantum criticality
• Heisenberg frustrated magnets: a nonperturbative approach
• Double-layer quantum Hall antiferromagnetism at filling fraction nu=2/(odd integer)
• Quasiparticle States at a d-Wave Vortex Core in High-Tc Superconductors: Induction of Local Spin Density Wave Order
• Evidence for Static Magnetism in the Vortex Cores of Ortho-II YBa${}_2$Cu${}_3$O${}_{6.50}$
• Canted antiferromagnetic and spin singlet quantum Hall states in double-layer systems
• Ground states of quantum antiferromagnets in two dimensions
• Doped planar quantum antiferromagnets with striped phases
• Quantum Phase Transitions and Conserved Charges
• Bond operator theory of doped antiferromagnets: from Mott insulators with bond-centered charge order, to superconductors with nodal fermions
• Vortex Structure in Underdoped Cuprates
• Anomalous Proximity Effect in Underdoped YBaCuO Josephson Junctions
• Thermodynamics of the interplay between magnetism and high-temperature superconductivity
• Proximity Effect and Josephson Coupling in the SO(5) Theory of High-Tc Superconductivity
• Pinning of dynamic spin density wave fluctuations in the cuprate superconductors
• Unified Description of the Resonance Peak and Incommensuration in High-$T_c$ Superconductors
• The Structure of a Vortex in the t-J Model
• Pi excitation of the t-J model
• Microscopic Electron Models with Exact SO(5) Symmetry
• Where is the pi particle?
• Hole concentration dependence of the magnetic moment in superconducting and insulating La2-xSrxCuO4
• Topological doping and the stability of stripe phases
• Staggered local density-of-states around the vortex in underdoped cuprates
• Theory of Magnetic Field Induced Spin Density Wave in High Temperature Superconductors
• Nodal quasi-particles and coexisting orders in striped superconductors
• Comment on "Bicritical and Tetracritical Phenomena and Scaling Properties of the SO(5) Theory"
• Finite-Size Studies on the SO(5) Symmetry of the Hubbard Model
• Quantum phase transitions in cuprates: stripes and antiferromagnetic supersolids
• SO(5) theory of insulating vortex cores in high-$T_c$ materials
• Multicritical Phenomena of Superconductivity and Antiferromagnetism in Organic Conductor $\kappa$-(BEDT-TTF)${}_2$X
• Fractionalization patterns in strongly correlated electron systems: Spin-charge separation and beyond
• Vortex state in a doped Mott insulator
• Theory of NMR as a local probe for the electronic structure in the mixed state of the high-$T_c$ cuprates
• Spin-lattice relaxation in the mixed state of YBaCuO: Can we see Doppler-shifted d-wave quasiparticles?
• A Duality Between Unidirectional Charge Density Wave Order and Superconductivity
• Quantum phase transitions in antiferromagnets and superfluids
• Search for the πResonance in Two Particle Tunneling Experiments of YBCO Superconductors
• Bond and Neel order and fractionalization in ground states of easy-plane antiferromagnets in two dimensions
• Antiferromagnetic hedgehogs with superconducting cores
• Excitations in antiferromagnetic cores of superconducting vortices
• Nuclear spin-spin coupling in La_{2-x}Sr_{x}CuO_{4} studied by stimulated echo decay
• Intrinsic resistivity and the SO(5) theory of high-temperature superconductors
• Vortex lattice stability in the SO(5) model

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• Effect of weak disorder on the phase competition in iron pnictides
• Induced spin-triplet pairing in the coexistence state of antiferromagnetism and singlet superconductivity: collective modes and microscopic properties
• The phase diagram of the underdoped cuprates at high magnetic field
• Co-doping effects on magnetism and superconductivity in the 112-type EuFeAs2 system
• Magnetic field resonantly enhanced free spins in underdoped YBa${}_2$Cu${}_3$O${}_{6+x}$
• Phenomenological lattice model for dynamic spin and charge fluctuations in the cuprates
• Phase diagram of the three band half-filled Cu-O two-leg ladder
• Collective mode in the SU(2) theory of cuprates
• Fluctuations and Higgs mechanism in Under-Doped Cuprates: a Review
• Spiral to stripe transition in the two-dimensional Hubbard model
• Three-dimensional Abelian and non-Abelian gauge Higgs theories
• Field-theory results for three-dimensional transitions with complex symmetries
• ARPES, Neutrons, and the High-$T_c$ Mechanism
• Quenching the Superconducting State of Cuprate Compounds with Electric Currents: A Variational Study
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