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Superconducting order of Sr2RuO4 from a three-dimensional microscopic model

Henrik S. Røising, Thomas Scaffidi, Felix Flicker, Gunnar F. Lange, and Steven H. Simon
Phys. Rev. Research 1, 033108 – Published 18 November 2019
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  • INTRODUCTION
  • EFFECTIVE THREE-DIMENSIONAL MODEL
  • WEAK-COUPLING THEORY
  • RESULTS AND DISCUSSION
  • CONCLUSIONS
  • ACKNOWLEDGMENTS
    • References

    Abstract

    We compute and compare even- and odd-parity superconducting order parameters of strontium ruthenate (Sr2RuO4) in the limit of weak interactions, resulting from a fully microscopic three-dimensional model including spin-orbit coupling. We find that odd-parity helical and even-parity d-wave order are favored for smaller and larger values of the Hund's coupling parameter J, respectively. Both orders are found compatible with specific heat data and the recently reported nuclear magnetic resonance (NMR) Knight shift drop [A. Pustogow et al., Nature 574, 72 (2019)]. The chiral p-wave order, numerically very competitive with helical order, sharply conflicts with the NMR experiment.

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    • Received 1 August 2019

    DOI:https://doi.org/10.1103/PhysRevResearch.1.033108

    Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

    Published by the American Physical Society

    Physics Subject Headings (PhySH)

    1. Research Areas
    Magnetic susceptibilityMultiband superconductivitySpecific heatSuperconducting order parameter
    1. Physical Systems
    RuthenatesStrongly correlated systemsUnconventional superconductors
    1. Techniques
    Renormalization groupTight-binding model
    Condensed Matter, Materials & Applied Physics

    Authors & Affiliations

    Henrik S. Røising1,*, Thomas Scaffidi2,3, Felix Flicker1, Gunnar F. Lange1,4, and Steven H. Simon1

    • 1Rudolf Peierls Center for Theoretical Physics, Oxford OX1 3PU, United Kingdom
    • 2Department of Physics, University of California, Berkeley, California 94720, USA
    • 3Department of Physics, University of Toronto, Toronto, Ontario M5S 1A7, Canada
    • 4TCM Group, Cavendish Laboratory, University of Cambridge, Cambridge CB3 0HE, United Kingdom

    • *henrik.roising@physics.ox.ac.uk

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    Vol. 1, Iss. 3 — November - December 2019

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    • Figure 1
      Figure 1

      Tight-binding fit to the 17-band model of Ref. [26]. The inset indicates paths and high-symmetry points in the Brillouin zone, using a primitive tetragonal unit cell. The crosses mark the chosen fitting points, i.e., the k path.

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    • Figure 2
      Figure 2

      (a)–(c) Fermi surfaces with the effective model, with the color referring to the orbital content |uxzμ(k)|2+|uyzμ(k)|2. The α sheet is dominated by the dxz and dyz orbitals, β is mostly dominated by dxz and dyz, and γ band mostly by dxy, but strong mixing takes place along the Γ−M line for the two latter bands (cf. Ref. [26]). Relative densities produced with this model: ρα/ρtot=0.160, ρβ/ρtot=0.334, and ργ/ρtot=0.506 (cf. Ref. [36]). (d), (e) kz slices of the Fermi surfaces with the effective model compared with the 17-band model. The cuts are taken at (d) kz=0, and (e) kz=2π. (f) The band structure of the 17-band model in Ref. [26], which is based on spin-resolved ARPES data.

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    • Figure 3
      Figure 3

      Eigenvalues of the leading order parameter in each irreducible representation: A1g, extended s-wave singlet; B1g, B2g, d-wave singlet; A2g, g-wave singlet; Eu, chiral p-wave triplet; and A1u, A2u, B1u, B2u, helical p-wave triplet.

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    • Figure 4
      Figure 4

      (a)–(c) |Δμ(k)| for the leading helical order parameter (A1u) at J/U=0.06, and (d)–(f) for the leading even-parity order parameter (B1g) at J/U=0.20.

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    • Figure 5
      Figure 5

      Cuts for three values of kz, showing the magnitude of the helical order parameter at J/U=0.06. Here, θ is the in-plane polar angle, defined with vertex at (0,0,kz/2) for β and γ, and vertex at (π,π,kz/2) for α.

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    • Figure 6
      Figure 6

      Same as described in the caption of Fig. 5, but here showing the signed B1g order parameter at J/U=0.20.

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    • Figure 7
      Figure 7

      Specific heat C divided by temperature T and normal state value γn, calculated for leading (a) helical triplet order with J/U=0.06 and (b) d-wave singlet order with J/U=0.20. The black dots are experimental values adapted from Ref. [13].

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    • Figure 8
      Figure 8

      The temperature dependence of the calculated magnetic susceptibilty (normalized by the normal state value) for three relevant order parameters, A1u and Eu orders at J/U=0.06, and B1g order at J/U=0.20. (a) External field pointing in the basal plane. NMR Knight shift data from Ref. [66] for two different Oxygen sites are plotted along with the calculated magnetic susceptibility. (b) External field pointing out of the basal plane.

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