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Antiferomagnetism and triplet superconductivity in Bechgaard salts

Antiferomagnetism and triplet superconductivity in Bechgaard salts. Daniel Podolsky (Harvard and UC Berkeley) Timofey Rostunov (Harvard) Ehud Altman (Harvard) Antoine Georges (Ecole Polytechnique) Eugene Demler (Harvard). References: Phys. Rev. Lett. 93:246402 (2004)

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Antiferomagnetism and triplet superconductivity in Bechgaard salts

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  1. Antiferomagnetism and triplet superconductivity in Bechgaard salts Daniel Podolsky (Harvard and UC Berkeley) Timofey Rostunov (Harvard) Ehud Altman (Harvard) Antoine Georges (Ecole Polytechnique) Eugene Demler (Harvard) References: Phys. Rev. Lett. 93:246402 (2004) Phys. Rev. B 70:224503 (2004) cond-mat/0506548

  2. Outline • Introduction. Phase diagram of Bechgaard salts • New experimental tests of triplet superconductivity • Antiferomagnet to triplet superconductor transition • in quasi 1d systems. SO(4) symmetry • Implications of SO(4) symmetry for the phase diagram. • Comparison to (TMTSF)2PF6 • Experimental test of SO(4) symmetry

  3. Bechgaard salts Stacked molecules form 1d chains Jerome, Science 252:1509 (1991)

  4. Evidence for triplet superconductivity in Bechgaard salts • Strong suppression of Tc by disorder Choi et al., PRB 25:6208 (1982) Tomic et al., J. Physique 44: C3-1075 (1982) Bouffod et al, J. Phys. C 15:2951 (1981) • Superconductivity persists at fields • exceeding the paramagnetic limit Lee et al., PRL 78:3555 (1997) Oh and Naughton, cond-mat/0401611 • No suppression of electron spin • susceptibility below Tc. NMR Knight • shift study of 77S in (TMTSF)2PF6 Lee et al, PRL 88:17004 (2002)

  5. - + - + - + - + P-wave superconductor without nodes Order parameter py px Specific heat in (TMTSF)2PF6 Garoche et al., J. Phys.-Lett. 43:L147 (1982)

  6. Nuclear spin lattice relaxation ratein (TMTSF)2PF6 Lee et al., PRB 68:92519 (2003) For (TMTSF)2ClO4 similar behavior has been observed by Takigawa et.al. (1987) Typically this would be attributed to nodal quasiparticles (nodal line) This work: T3 behavior of 1/T1 due to spin waves

  7. Spin waves in triplet superconductors Spin wave: d-vector rotates In space Dispersion of spin waves Full spin symmetry Easy axis anisotropy

  8. Spin anisotropy of the triplet superconducting order parameter Spin anisotropy in the antiferromagnetic state: Torrance et al. (1982) Dumm et al. (2000) Spin z axis points along the crystallographic b axis. Assuming the same anistropy in the superconducting state Easy direction for the superconducting order parameter is along the b axis For Bechgaard salts we estimate

  9. Moriya relation: -- nuclear Larmor frequency Experimental regime of parameters Contribution of spin waves to 1/T1 Creation or annihilation of spin waves does not contribute to T1-1 Scattering of spin waves contributes toT1-1

  10. Contribution of spin waves to 1/T1 (1) (2) is the density of states for spin wave excitations. Using For we can take where is the dimension This result does not change when we include coherence factors

  11. Contribution of spin waves to 1/T1 • For small fields, T1-1 depends on the direction of the magnetic field • When , we have T3 scaling of T1-1 in d=2 • When , we have exponential suppression of T1-1 These predictions of the spin-wave mechanism of nuclear spin relaxation can be checked in experiments

  12. S=1 Sz=0 S=1 Sx=0 S=1 Sy=0 For Bechgaard salts we estimate Spin-flop transition in the triplet superconducting state At B=0 start with (easy axis). For this state does not benefit from the Zeeman energy. For the order parameter flops into the xy plane. This state can benefit from the Zeeman energy without sacrificing the pairing energy.

  13. Field and direction dependent Knight shift in UPt3 Tau et al., PRL 80:3129 (1998)

  14. Competition of antiferomagnetism and triplet superconductivity in Bechgaard salts

  15. Coexistence of superconductivity and magnetism Vuletic et al., EPJ B25:319 (2002)

  16. Interacting electrons in 1d Interaction Hamiltonian Ls’ Ls’ Ls’ Ls’ Rs’ Rs’ Ls’ Rs’ g1 g2 g4 g4 Ls Ls Rs Ls Rs Rs Rs Rs Phase diagram g1 SDW/TSC transition at Kr=1. This corresponds to SDW (CDW) TSC (SS) 2 1/2 1 Kr 2g2 = g1 CDW (SS) SS (CDW) SS CDW

  17. Symmetries Spin SO(3)S algebra SO(3)S is a good symmetry of the system Isospin SO(3)I symmetry We always have charge U(1) symmetry When Kr=1, U(1) is enhanced to SO(3)I because

  18. transforms as a vector under spin and isospin rotations spin isospin SO(4)=SO(3)SxSO(3)Isymmetry.Unification of antiferromagnetism and triplet superconductivity. Order parameter for antiferromagnetism: Order parameter for tripletsuperconductivity:

  19. Two separate SO(3) algebras Isospin group SO(4)I= SO(3)RxSO(3)L SO(3)SxSO(4)I symmetry at incommensurate filling Umklapp scattering reduces SO(4)I to SO(3)I

  20. Role of interchain hopping

  21. Ginzburg-Landaufree energy SO(4) symmetry requires SO(4) symmetric GL free energy Weak coupling analysis

  22. Unitary TSC for . TSC order parameter r1 r2 AF unitary TSC GL free energy. Phase diagram First order transition between AF and TSC

  23. Unitary TSC and AF. Thermal fluctuations Extend spin SO(3) to SO(N). Do large N analysis in d=3 r1 AF r2 Unitary TSC • First order transition between normal and triplet superconducting • phases (analogous result for 3He: Bailin, Love, Moore (1997)) • Tricritical point on the normal/antiferromagnet boundary

  24. T T Normal Normal AF AF TSC TSC P “V” Triplet superconductivity and antiferromagnetism.Phase diagram First order transition becomes a coexistence region Phase diagram of Bechgaard salts Vuletic et al., EPJ B25:319 (2002)

  25. Experimental test of quantum SO(4) symmetry Q operator rotates between AF and TSC orders q-mode should appear as a sharp resonance in the TSC phase Energy of the q mode softens at the first order transition between superconducting and antiferromagnetic phases

  26. Conclusions • New experimental tests of triplet pairing in Bechgaard salts: • 1) NMR for T < 50mK and small fields. Expect strong suppression • of 1/T1 • 2) Possible spin flop transtion for magnetic fields • along the b axis and field strength around 0.5 kG • 3) Microwave resonance in Bechgaard salts at . • (For Sr2RuO4 expect such resonance at ) • SO(4) symmetry is generally present at the antiferromagnet • to triplet superconductor transition in quasi-1d systems • SO(4) symmetry helps to explain the phase diagram of (TMTSF)2PF6 • SO(4) symmetry implies the existence of a new collective mode, • the q resonance. The q resonance should be observable using • inelastic neutron scattering experiments (in the superconducting • state)

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