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Chiral superconductivity from repulsive interactions in doped graphene

Nature Physics volume 8, pages 158163 (2012) | Download Citation

Abstract

Chiral superconductivity, which breaks time-reversal symmetry, can exhibit a wealth of fascinating properties that are highly sought after for nanoscience applications. We identify doped graphene monolayer as a system where chiral superconductivity can be realized. In this material, a unique situation arises at a doping where the Fermi surface is nested and the density of states is singular. In this regime, d-wave superconductivity can emerge from repulsive electron–electron interactions. Using a renormalization group method, we argue that superconductivity dominates over all competing orders for generic weak repulsive interactions. Superconductivity develops simultaneously in two degenerate d-wave pairing channels. We argue that the resulting superconducting state is of chiral type, with the phase of the superconducting order parameter winding by 4π around the Fermi surface. Realization of this state in doped graphene will prove that superconductivity can emerge from electron–electron repulsion, and will open the door to applications of chiral superconductivity.

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References

  1. 1.

    , , , & The electronic properties of graphene. Rev. Mod. Phys. 81, 109–162 (2009).

  2. 2.

    , , & Electronic transport in two-dimensional graphene. Rev. Mod. Phys. 83, 407–470 (2011).

  3. 3.

    Viewpoint: Peeling back the layers or doubling the stakes? Calculations of bilayer graphene reveal the possibility of new electronic phases. Physics 3, 1 (2010).

  4. 4.

    Kohn–Luttinger superconductivity in graphene. Phys. Rev. B 78, 205431 (2008).

  5. 5.

    & Pomeranchuk instability in doped graphene. New. J. Phys. 10, 113009 (2008).

  6. 6.

    & Itinerant electron-driven chiral magnetic ordering and spontaneous quantum Hall effect in triangular lattice models. Phys. Rev. Lett. 101, 156402 (2008).

  7. 7.

    Spontaneous quantum Hall effect in quarter doped Hubbard model on honeycomb lattice and its possible realization in quarter doped graphene system. Preprint at (2011).

  8. 8.

    , , & Spin-density-wave instability in graphene doped near the van Hove singularity. Phys. Rev. B 84, 125404 (2011).

  9. 9.

    Quantized hall effect in superfluid helium-3 film. Phys. Lett. A 128, 277–279 (1988).

  10. 10.

    & Phenomenological theory of unconventional superconductivity. Rev. Mod. Phys. 63, 239–311 (1991).

  11. 11.

    , & Quantum phase transitions in d-wave superconductors. Phys. Rev. Lett. 85, 4940–4943 (2000).

  12. 12.

    & Nonabelions in the fractional quantum hall effect. Nucl. Phys. B360, 362–396 (1991).

  13. 13.

    Non-Abelian statistics of half-quantum vortices in p-wave superconductors. Phys. Rev. Lett. 86, 268–271 (2001).

  14. 14.

    & Superconducting proximity effect and Majorana fermions at the surface of a topological insulator. Phys. Rev. Lett. 100, 096407 (2008).

  15. 15.

    , , & Time-reversal-invariant topological superconductors and superfluids in two and three dimensions. Phys. Rev. Lett. 102, 187001 (2009).

  16. 16.

    , , & Stable topological superconductivity in a family of two-dimensional fermion models. Phys. Rev. B 81, 024504 (2010).

  17. 17.

    & Mutual friction in superfluid 3He: Effects of bound states in the vortex core. Phys. Rev. B 44, 9667–9677 (1991).

  18. 18.

    & Fractional charge, spin and statistics of solitons in superfluid 3He film. J. Phys. Condens. Matter 1, 5263–5274 (1989).

  19. 19.

    Magnetic induction of dx2y2+idxy order in high-Tc superconductors. Phys. Rev. Lett. 80, 5188–5191 (1998).

  20. 20.

    On edge states in superconductors with time inversion symmetry breaking. J. Exp. Theor. Phys. Lett. 66, 522–527 (1997).

  21. 21.

    , & Spin quantum Hall effect in unconventional superconductors. Phys. Rev. B 60, 4245–4254 (1999).

  22. 22.

    & Superconductors with broken time-reversal symmetry: Spontaneous magnetization and quantum Hall effects. Phys. Rev. B 68, 214503 (2003).

  23. 23.

    , & Non-Abelian topological orders and Majorana fermions in spin-singlet superconductors. Phys. Rev. B 82, 134521 (2010).

  24. 24.

    , , & Superconducting phase with a chiral f-wave pairing symmetry and Majorana fermions induced in a hole-doped semiconductor. Phys. Rev. Lett. 106, 157003 (2011).

  25. 25.

    & The superconductivity of Sr2RuO4 and the physics of spin-triplet pairing. Rev. Mod. Phys. 75, 657–712 (2003).

  26. 26.

    & Resonating valence bonds and mean-field d-wave superconductivity in graphite. Phys. Rev. B 75, 134512 (2007).

  27. 27.

    & Superconducting states of pure and doped graphene. Phys. Rev. Lett. 98, 146801 (2007).

  28. 28.

    & New mechanism for superconductivity. Phys. Rev. Lett. 15, 524–526 (1965).

  29. 29.

    Superconductivity and antiferromagnetism in the two-dimensional Hubbard model: Scaling theory. Europhys. Lett. 4, 609–615 (1987).

  30. 30.

    Maximal increase of the superconducting transition temperature due to the presence of van Hove singularities. Sov. Phys. JETP 66, 848–854 (1987).

  31. 31.

    , & Truncation of a two-dimensional Fermi surface due to quasiparticle gap formation at the saddle points. Phys. Rev. Lett. 81, 3195–3198 (1998).

  32. 32.

    et al. Extended van Hove singularity and superconducting instability in doped graphene. Phys. Rev. Lett. 104, 136803 (2010).

  33. 33.

    et al. Liquid-gated interface superconductivity on an atomically flat film. Nature Mater. 9, 125–128 (2010).

  34. 34.

    & Superconductivity close to the Mott state: From condensed-matter systems to superfluidity in optical lattices. Ann. Phys. 324, 1452–1515 (2009).

  35. 35.

    & Renormalization group flow, competing phases and the structure of superconducting gap in multiband models of iron-based superconductors. Phys. Rev. B 82, 214515 (2010).

  36. 36.

    , , & Mechanism for explaining differences in the order parameters of FeAs-based and FeP-based pnictide superconductors. Phys. Rev. Lett. 106, 187003 (2011).

  37. 37.

    The band theory of graphite. Phys. Rev. 71, 622–634 (1947).

  38. 38.

    Superconductivity by long-range colour magnetic interaction in high-density quark matter. Phys. Rev. D 59, 094019 (1999).

  39. 39.

    & Quantum-critical pairing with varying exponents. J. Low Temp. Phys. 161, 263–281 (2010).

  40. 40.

    , & Possible high-temperature superconducting state with a d+id pairing symmetry in doped graphene. Phys. Rev. B 81, 085431 (2010).

  41. 41.

    Density waves and Cooper pairing on the honeycomb lattice. Phys. Rev. Lett. 100, 146404 (2008).

  42. 42.

    & Unconventional superconductivity on honeycomb lattice: Theory of Kekule order parameter. Phys. Rev. B 82, 035429 (2010).

  43. 43.

    & Introduction to Unconventional Superconductivity 69 (Gordon and Breach Science Publishers, 1998).

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Affiliations

  1. Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA

    • Rahul Nandkishore
    •  & L. S. Levitov
  2. Department of Physics, University of Wisconsin-Madison, Madison, Wisconsin 53706, USA

    • A. V. Chubukov

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Contributions

R.N., L.S.L. and A.V.C. jointly identified the problem, performed the analysis and wrote the paper.

Competing interests

The authors declare no competing financial interests.

Corresponding author

Correspondence to A. V. Chubukov.

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https://doi.org/10.1038/nphys2208

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