Antiferomagnetism and triplet superconductivity in Bechgaard salts

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. 93246402
(2004) Phys. Rev. B
70224503 (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 2521509 (1991)
4
Evidence for triplet superconductivity in
Bechgaard salts

• Strong suppression of Tc by disorder

Choi et al., PRB 256208 (1982) Tomic et al., J.
Physique 44 C3-1075 (1982) Bouffod et al, J.
Phys. C 152951 (1981)

• Superconductivity persists at fields
• exceeding the paramagnetic limit

Lee et al., PRL 783555 (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 8817004 (2002)
5
P-wave superconductor without nodes
Order parameter
py
px
Specific heat in (TMTSF)2PF6
Garoche et al., J. Phys.-Lett. 43L147 (1982)
6
Nuclear spin lattice relaxation ratein
(TMTSF)2PF6
Lee et al., PRB 6892519 (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
Easy axis anisotropy
Full spin symmetry
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
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Contribution of spin waves to 1/T1
Creation or annihilation of spin waves does not
contribute to T1-1
Scattering of spin waves contributes to T1-1
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
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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 d2
• 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
Spin-flop transition in the triplet
superconducting state
At B0 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 803129 (1998)
14
Competition of antiferomagnetism and triplet
superconductivity in Bechgaard salts
15
Coexistence of superconductivity and magnetism
Vuletic et al., EPJ B25319 (2002)
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Interacting electrons in 1d
Interaction Hamiltonian
Ls
Ls
Ls
Ls
Rs
Rs
Ls
Rs
g1
g2
g4
g4
Rs
Ls
Ls
Ls
Rs
Rs
Rs
Rs
Phase diagram
g1
SDW/TSC transition at Kr1. This corresponds to
SDW (CDW)
TSC (SS)
1/2
2
1
Kr
2g2 g1
CDW (SS)
SS (CDW)
SS
CDW
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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 Kr1, U(1) is enhanced to SO(3)I because
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SO(4)SO(3)SxSO(3)I symmetry.Unification of
antiferromagnetism and triplet superconductivity.
Order parameter for antiferromagnetism
Order parameter for triplet superconductivity
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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-Landau free energy
SO(4) symmetry requires
SO(4) symmetric GL free energy
Weak coupling analysis
22
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 d3
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
Triplet superconductivity and antiferromagnetism.
Phase diagram
First order transition becomes a coexistence
region
Phase diagram of Bechgaard salts
Vuletic et al., EPJ B25319 (2002)
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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 lt 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)