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Tunnelling in triplet superconductors

Tunnelling in triplet superconductors. C. Bolech (Geneva/Rice U.) T. Giamarchi (Geneva). Organic (super-) conductors. TM 2 (X) family. Strongly correlated at high T. Nature of Superconductivity at low T ?. TG Chem. Rev. 104 5037 (2004).

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Tunnelling in triplet superconductors

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  1. Tunnelling in triplet superconductors C. Bolech (Geneva/Rice U.) T. Giamarchi (Geneva)

  2. Organic (super-) conductors TM2(X) family • Strongly correlated at high T Nature of Superconductivity at low T ? TG Chem. Rev. 104 5037 (2004)

  3. Evidence for triplet superconductivity in organic salts • Suppression of superconductivity by non-magnetic impurities [Joo et al (2004)] • Upper critical fields in excess of the Pauli-Clogston paramagnetic limit [Lee et al. (2002)] • NMR Knight-shift [Lee et al. (2002)] No final answer

  4. Tunnelling as a probe • Phase sensitive experiments difficult • Simple tunnelling • Needs a good theory of tunnelling

  5. Mid gap states • Planar junctions: Sengupta et al. PRB (2001) Andreev bound states Mid gap states • Magnetic field on ZBA Tanuma et al. PRB (2002)

  6. STM Bicrystal Junctions and STM M.J. Naughton Synth. Metals 137 1215 (2003)

  7. Model • Point contact junction • Normal, singlet or triplet lead

  8. One dimensional approximation • Spatial structure not important • 1D leads enough for p-wave • Right and Left movers

  9. with Hamiltonian BCS approximation for the leads

  10. How to treat • Semiconductor band models [Blonder-Tinkham-Klapwijk] • Density of state • Good qualitative agreement • No connection to microscopic parameters • First Microscopic Keldysh formulations(e.g. Cuevas-Martın-Rodero-Yeyati PRB 1996) • Good quantitative agreement with experiments • Heavy beyond the s-wave case

  11. Semiclassical methods • More versatile but not good for anisotropic cases • direct solution of Keldysh action (C. J. Bolech + TG, PRL 92 127001 (2004) ; PRB 71 024517 (2005); cond-mat/0508177 ) • Simpler • Treat both single particle and Andreev tunnelling • Allows to treat triplet case • Allows to treat magnetic field and temperature

  12. Splitting Normal-Singlet tunneling t = 0.2 (lower); t=0.5 (upper)

  13. B //  Normal-Triplet tunneling

  14. B ? Singlet-Triplet tunneling Red Curve: zero-field I-V

  15. Triplet-Triplet tunneling Red Curve: zero-field I-V t=0.2 (upper) t=0.5 (lower)

  16. S-T H//a : no splitting H //b: splitting (T) Test for triplet N-S or N-T H H Singlet: splitting Triplet: no splitting

  17. Conclusions • Good method to treat point contact tunnelling • Proposal to detect triplet superconductivity in Bechgaard salts • Temperature • Pair breaking close to surface in more isotropic systems (Ruthenates, etc.)

  18. Keldysh representation • Action for each lead (1 and 2) : 8 £ 8 spinor

  19. Tunnelling term Current:

  20. Invert the action • Block diagonal in frequencies • Soft cutoff in Andreev reflections

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