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Antiferromagnetism and charged vortices in high-Tc superconductors

Daniel Knapp, Catherine Kallin, Amit Ghosal, and Sarah Mansour
Phys. Rev. B 71, 064504 – Published 8 February 2005
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  • INTRODUCTION
  • MODEL AND METHOD
  • RESULTS
  • SUMMARY AND CONCLUSIONS
  • ACKNOWLEDGEMENTS
  • APPENDICES
    • References

    Abstract

    The effect of the long-range Coulomb interaction on charge accumulation in antiferromagnetic vortices in high-Tc superconductors is studied within a Bogoliubov–de Gennes mean-field model of competing antiferromagnetic and d-wave superconducting orders. Antiferromagnetism is found to be associated with an accumulation of charge in the vortex core, even in the presence of the long-range Coulomb interaction. The manifestation of Π-triplet pairing in the presence of coexisting d-wave superconductivity and antiferromagnetic order, and the intriguing appearance of one-dimensional stripelike ordering are discussed. The local density of states in the vortex core is calculated and is found to be in excellent qualitative agreement with experimental data.

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    • Received 28 September 2004

    DOI:https://doi.org/10.1103/PhysRevB.71.064504

    ©2005 American Physical Society

    Authors & Affiliations

    Daniel Knapp1,*, Catherine Kallin1, Amit Ghosal2, and Sarah Mansour1,†

    • 1Department of Physics and Astronomy, McMaster University, Hamilton, Ontario, Canada L8S 4M1
    • 2Department of Physics, Duke University, North Carolina 27708-0305, USA

    • *Electronic address: dan@danielk.ca
    • †Current address: Department of Biochemistry, University of Toronto Hospital for Sick Children, 555 University Avenue, Toronto, Ontario, Canada M5G 1X8.

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    Issue

    Vol. 71, Iss. 6 — 1 February 2005

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    Images

    • Figure 1
      Figure 1
      (Color online) From left to right, electron number density relative to the average density δ⟨ni⟩=⟨ni⟩−0.875, for V=0, 0.2, and 0.35 on one half of a 20×40 unit cell (the other half is equivalent by symmetry) for an interaction strength J=1.15. For V=0.2 a region of reduced electron density screens the peak in the core. At V=0.35 the vortex core charge and the screening charge have changed sign, and modulations in the electron density have a much smaller amplitude (on the order of 10−3 electrons per site). The bottom row shows two-dimensional (2D) density plots of the 3D plots in the top row.Reuse & Permissions
    • Figure 2
      Figure 2
      (Color online) From left to right, the AFM order mi (in units of t) for V=0, 0.2, and 0.35 on one half of a 20×40 unit cell, with J=1.15 and nave=0.875. With V=0.2 the magnitude of the AFM has been approximately halved and at V=0.35, where the vortex core is no longer negatively charged, the AFM order is negligible. The shape of the AFM order is unaffected by the dramatic changes in the structure of the electron density induced by the LRC interaction. The bottom row shows 2D density plots of the 3D plots in the top row.Reuse & Permissions
    • Figure 3
      Figure 3
      (Color online) From left to right, the magnitude of the dSC order ∣Δi∣ (in units of t) for V=0, 0.2, and 0.35 on one half of a 20×40 unit cell, with J=1.15 and nave=0.875. The structure of ∣Δi∣ is unchanged by the LRC, but the magnitude is gradually reduced due to weakening of the nearest-neighbor attraction that generates the dSC pairing. The bottom row shows 2D density plots of the 3D plots in the top row. One can see that the coherence length ξ increases as the strength of the d-wave pairing is reduced.Reuse & Permissions
    • Figure 4
      Figure 4
      Peak values of dSC∣Δ0∣ (◻) far from the vortex core, and AFM ∣mcore∣ (엯) and electron density δ⟨ncore⟩ (▵) at the center of the vortex core as a function of increased LRC strength V, for a 20×40 unit cell with J=1.15 and nave=0.875. All quantities are plotted relative to their V=0 values. Between V=0.3 and V=0.35, the density of electrons in the core crosses over from positive to negative and the AFM order disappears. Lines are a guide to the eye.Reuse & Permissions
    • Figure 5
      Figure 5
      (Color online) Antiferromagnetic order mcore (dotted lines), in units of t, and electron number density δ⟨ncore⟩ (solid lines) at the center of the vortex core as a function of unit cell size L×2L for LRC strengths of V=0 (엯), V=0.15 (◻), and V=0.25 (◇), with J=1.15 and nave=0.875. When V=0 the density at the core increases toward half filling (0.125 in this plot) with increasing unit cell size. For V>0 the dependence becomes non-monotonic with the peak charge density occurring in the 22×44 unit cell. The anomalous increase in the AFM at V=0.25 for L=24, 26 is due to the development of a 1D anisotropy discussed in sec. 3E. Lines are a guide to the eye.Reuse & Permissions
    • Figure 6
      Figure 6
      (Color online) Antiferromagnetic order mcore (dotted lines) in units of t, and electron number density δ⟨ncore⟩ (solid lines) at the center of the vortex core as a function of the average density nave for LRC strengths of V=0 (엯), V=0.15 (◻), and V=0.25 (◇) for a 20×40 unit cell with J=1.15. The region containing AFM and negatively charged vortices shrinks slowly at first and then rapidly toward half filling with increasing V. Lines are a guide to the eye.Reuse & Permissions
    • Figure 7
      Figure 7
      (Color online) From left to right, electron number density δ⟨ni⟩=⟨ni⟩−0.875, AFM order mi, and dSC order ∣Δi∣ for an interaction strength J=1.3 and a LRC strength V=0.35 on one half of a 20×40 unit cell. The bottom row shows 2D density plots of the same. Both the electron density and the AFM order show a strong anisotropy, while the dSC order is only mildly affected. Note that, in contrast to the J=1.15 results for V=0.35, the AFM order survives and the charge density is negative at the vortex core.Reuse & Permissions
    • Figure 8
      Figure 8
      (Color online) The local density of states at the center of the vortex core (top), away from the vortex core along the node direction (middle), and averaged over all sites within a coherence length from the vortex center (bottom), for J=1.15 and nave=0.875 on a 26×52 unit cell. Solid lines are for V=0.15 and dashed lines are for V=0. The lines have been shifted vertically for clarity.Reuse & Permissions
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