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Mixed state of a π-striped superconductor

M. Zelli, Catherine Kallin, and A. John Berlinsky
Phys. Rev. B 84, 174525 – Published 29 November 2011
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  • INTRODUCTION
  • THE MODEL AND METHOD
  • RESULTS IN A MAGNETIC FIELD
  • SPECIFIC HEAT
  • DISCUSSION AND CONCLUSION
  • ACKNOWLEDGEMENTS
  • APPENDICES
    • References

    Abstract

    A model of an antiphase modulated d-wave superconductor has been proposed to describe the decoupling between Cu-O planes in 1/8 doped La2−xBaxCuO4. Unlike a uniform d-wave superconductor, this model exhibits an extended Fermi surface. Within Bogoliubov–de Gennes theory, we study the mixed state of this model and compare it to the case of a uniform d-wave superconductor. We find a periodic structure of the low-energy density of states, with a period that is proportional to B, corresponding to Landau levels that are a coherent mixture of particles and holes. These results are also discussed in the context of experiments which observe quantum oscillations in the cuprates, and are compared to those for models in which the Fermi surface is reconstructed due to translational symmetry breaking in the nonsuperconducting state and to a model of a Fermi-arc metal.

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    • Received 27 June 2011

    DOI:https://doi.org/10.1103/PhysRevB.84.174525

    ©2011 American Physical Society

    Authors & Affiliations

    M. Zelli*, Catherine Kallin, and A. John Berlinsky

    • Department of Physics and Astronomy, McMaster University, Hamilton, Canada

    • *zellim@mcmaster.ca

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    Issue

    Vol. 84, Iss. 17 — 1 November 2011

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    Images

    • Figure 1
      Figure 1
      Position dependence of the pairing gap for the bond-centered configuration using color coding on bonds. The circles in the middle of the plaquettes specify the positions of vortices for a l=8 magnetic field unit cell whose boundary is shown by the dashed line. In the singular gauge, the vortices at white (dark) circles are only seen by particles (holes). The lower part of the figure shows the varying gap amplitude as a function of x.Reuse & Permissions
    • Figure 2
      Figure 2
      DOS of a π-striped superconductor for various values of the pairing gap amplitude. The second nearest neighbor hopping for this DOS calculation is set to zero and the chemical potential μ is adjusted to yield 1/8 doping here and in the following figures unless another value is explicitly stated. Note the finite DOS at zero energy and the complex structure which arises from band folding associated with the strength of the periodic interaction as discussed in the text.Reuse & Permissions
    • Figure 3
      Figure 3
      The spectral weight (left) and FS (right) for four values of the pairing gap Δ (a) 0.05, (b) 0.1, (c) 0.2, and (d) 0.4 in half of the extended BZ. The colorbar applies only to the spectral weight.Reuse & Permissions
    • Figure 4
      Figure 4
      Low-energy DOS of a π-striped superconductor with Δ=0.01t and μ=−0.226 in the presence of magnetic fields of l=24 (top) and l=32 (bottom).Reuse & Permissions
    • Figure 5
      Figure 5
      DOS for Δ=0.25 and magnetic field of l=32 shown as a function of positive and negative energies separately. The band structure spans energies from −4−μ to 4−μ. However, the DOS is only shown in the −1<E<1 range.Reuse & Permissions
    • Figure 6
      Figure 6
      Low-energy DOS for Δ=0.25 and magnetic fields of l=40 (top) and l=32 (bottom).Reuse & Permissions
    • Figure 7
      Figure 7
      Low-energy Landau level spacing as a function of 1/l2 for Δ=0.25 and μ=−0.3. The spacing is defined as E(N)/N where E(N) is the minimum in the DOS between the Nth and N+1-th Landau levels and is shown for N=2 (triangle) and N=10 (circle). The line is a linear fit to the data that goes through the origin.Reuse & Permissions
    • Figure 8
      Figure 8
      The DOS structure in the absence of a magnetic field for Δ=0.25 and two dopings. Note the asymmetry at low E for 1/8 doping.Reuse & Permissions
    • Figure 9
      Figure 9
      Low-energy DOS for l=48 and Δ=0.2 and Δ=0.4. Landau levels are suppressed for Δ=0.4, but a sharp peak around E=0 appears.Reuse & Permissions
    • Figure 10
      Figure 10
      Density of electrons versus −μ for the magnetic field of l=16 and two cases of Δ=0.25 and Δ=0. Unlike Δ=0, the density does not exhibit a stepped behavior for Δ=0.25.Reuse & Permissions
    • Figure 11
      Figure 11
      Specific heat in the presence of various fields as a function of temperature for Δ=0.25 and μ=−0.3. The behavior of the curves at very low temperatures is significantly affected by the commensurability effect. The heavy line shows the specific heat in zero field for Δ=0 and μ=−0.225 corresponding to 1/8 doping. The slope associated with the linear behavior is about two times that of the slope for Δ=0.25 in zero field (noted by l=∞).Reuse & Permissions
    • Figure 12
      Figure 12
      Local density of electrons due to the low-energy states within 0.001t of E=0 for l=48 and Δ=0.4.Reuse & Permissions
    • Figure 13
      Figure 13
      High (red stripe) and low (blue stripe) density structure of the low-energy particles relative to the modulated d-wave gap. High (low) density is indicated by a red (blue) stripe.Reuse & Permissions
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