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-tunneling-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.''
Highlights
The determination of the ground state of the cuprate superconductors as a function of the hole density has been one of the central problems in condensed matter physics in the last decade
It is well established that the ground state is a Mott insulator with long-range magnetic Neel order
The excitons scatter off the vortex lattice, and our results describe the evolution of the resulting spectrum as one moves towards the onset of SDW order by increasing the applied magnetic field
Summary
The determination of the ground state of the cuprate superconductors as a function of the hole density has been one of the central problems in condensed matter physics in the last decade. Our primary assumption is that the low-energy collective excitations can be described using the theory of the vicinity of a quantum critical point between the SCϩSDW and the SC phases; evidence supporting this assumption was reviewed in Ref. 4 This critical point is present either as a function of ␦ in the material under consideration, or in a generalized parameter space but quite close to the physical axis. The experimental evidence[19,20] supports the conclusion the SDW ordering in the cuprates in collinear, but the present formalism allows a common treatment of both the collinear and spiral cases This complex-vector formulation of the SDW order allows treatment of the SDW quantum transition by a straightforward generalization of the real-vector theory used for the Neel state in the insulator; related points have been made by Castro Neto and Hone[21] and Zaanen.[22] The same approach was used by Zachar et al.[23] to treat the onset of SDW order at finite temperatures, as we will indicate below.
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