Research ArticleCONDENSED MATTER PHYSICS

Generalized Anderson’s theorem for superconductors derived from topological insulators

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Science Advances  28 Feb 2020:
Vol. 6, no. 9, eaay6502
DOI: 10.1126/sciadv.aay6502
  • Fig. 1 Material under consideration.

    (A) Schematic representation of the crystal structure for materials in the family of Bi2Se3 (view along the c axis); the gray rectangle depicts the reduced (monoclinic) symmetry in CPSBS (see discussion in section S4). (B) Side view of the QL unit, highlighting the specific choice of orbitals: Shown on the left are the top (T) and bottom (B) layer orbitals used in (18); shown on the right are the even (P1z+) and odd (P2z) parity orbitals used in this work, identified as symmetric and antisymmetric superpositions of the orbitals in the top/bottom layers.

  • Fig. 2 Possibilities of pairing.

    (A) Schematic representation of the gap structure in the orbital basis. The yellow and green colors correspond to P1z+ and P2z orbitals, respectively, as shown in Fig. 1 (B). The dotted lines represent pairing between electrons with opposite momenta. Left: Intraorbital singlet pairing for A1g. Middle: Interorbital triplet/singlet pairing for A1u/A2u. Right: Interorbital triplet pairing for Eu. (B) Schematic representation of the gap function in the band basis. Left: Fully gapped, for order parameters in A1g and A1u, as well as in A2u for a two-dimensional (2D) Fermi surface (FS). Right: Nodal gap structure for order parameters in A2u (for a 3D FS) and Eu. The red dot indicates the position of the nodes, which can be read off from table S3. For a 3D FS, these are point nodes on an ellipsoidal FS, while for a 2D FS, these are line nodes extending along the z direction on a cylindrical FS.

  • Fig. 3 Specific heat and thermal conductivity across Tc.

    (A) Temperature dependencies of the electronic specific heat cel of samples I and II (symbols), together with the theoretical curve for a line-nodal SC gap in the clean limit (30) assuming the SC volume fraction of 85 and 100%, respectively; horizontal lines correspond to γel. Note that despite the strong scatterings in these samples, the clean-limit theory describes the cel(T) data well, which is related to the robustness of the SC state against impurities. (B) Double-logarithmic plot of κ/T versus T for sample I measured in 0 and 3 T. (C) Schematics of the steady-state thermal-conductivity measurement setup.

  • Fig. 4 Ultralow-temperature thermal conductivity.

    (A and B) Plots of κ/T versus T2 for samples I and II measured in perpendicular magnetic fields up to 3 T. Dashed lines are the linear fits to the lowest-temperature part of the data; the intercept of these lines on the κ/T axis gives κ0/T. (C and D) Magnetic-field dependencies of the electronic heat-transport coefficient ae in samples I and II; solid lines mark the range of its change from 0 T to the normal state. The hatch at the bottom of (C) represents the expected background contributed by the non-SC portion of sample I.

Supplementary Materials

  • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/6/9/eaay6502/DC1

    Section S1. The concept of SC fitness and the effective scattering rate

    Section S2. The normal-state Hamiltonian for materials in the family of Bi2Se3

    Section S3. The order parameters for materials in the family of Bi2Se3

    Section S4. Analysis for C2h symmetry

    Section S5. Drude analysis of the scattering rates in Bi2Se3-based superconductors

    Section S6. Phononic contribution to the thermal conductivity

    Table S1. Parametrization of the normal-state Hamiltonian.

    Table S2. Superconducting order parameters for the materials in the family of Bi2Se3.

    Table S3. Analysis of the gap structure for the materials in the family of Bi2Se3.

    Table S4. Estimates of the scattering rates in Bi2Se3-based superconductors from the simple

    Drude analysis as was done for CPSBS in the main text.

    Fig. S1. Behavior of phonons.

  • Supplementary Materials

    This PDF file includes:

    • Section S1. The concept of SC fitness and the effective scattering rate
    • Section S2. The normal-state Hamiltonian for materials in the family of Bi2Se3
    • Section S3. The order parameters for materials in the family of Bi2Se3
    • Section S4. Analysis for C2h symmetry
    • Section S5. Drude analysis of the scattering rates in Bi2Se3-based superconductors
    • Section S6. Phononic contribution to the thermal conductivity
    • Table S1. Parametrization of the normal-state Hamiltonian.
    • Table S2. Superconducting order parameters for the materials in the family of Bi2Se3.
    • Table S3. Analysis of the gap structure for the materials in the family of Bi2Se3.
    • Table S4. Estimates of the scattering rates in Bi2Se3-based superconductors from the simple.
    • Drude analysis as was done for CPSBS in the main text.
    • Fig. S1. Behavior of phonons.

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