Pair Density Wave in the Pseudogap State

1
Pair Density Wave in the Pseudogap State of High
Temperature Superconductors
Handong Chen(Stanford) Oskar Vafek(Stanford) Ali
Yazdani(UIUC) Shoucheng Zhang(Stanford)
APS March Meeting Montreal, March 23 2004
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Theoretical Motivation

• For a superconductor with low superfluid
  density and short coherence length,
  superconductivity can be destroyed without
  breaking the hole pairs.
• The insulating hole pair crystal states can
  occur at commensurate fractional occupation
  numbers. In these states, the translation
  symmetry is spontaneously broken and the new unit
  cell has integral number of pairs.

H.D. Chen, S. Capponi, F. Alet and S.C. Zhang,
cond-mat/0312660
3
Hole pair crystal vs hole crystal

• For hole crystal, there is 1 hole per unit cell.
  If the unit cell is L x L, the doping is
• x1/(L x L).

• For hole pair crystal, there is 1 hole-pair (2
  holes) per unit cell. If the unit cell is L x L,
  the doping is x2/(L x L).

x 1/8 L 4
H.D. Chen et al., Phys. Rev. Lett. 89
137004(2002). H.C. Fu et al.,
cond-mat/0403001
4
Hole pair crystal vs hole crystal

• For hole crystal, there is 1 hole per unit cell.
  If the unit cell is L x L, the doping is
• x1/(L x L).

• For hole pair crystal, there is 1 hole-pair (2
  holes) per unit cell. If the unit cell is L x L,
  the doping is x2/(L x L).

x 1/16 L 4
H.D. Chen et al., Phys. Rev. Lett. 89
137004(2002). H.C. Fu et al.,
cond-mat/0403001
5
STM

• STM conductance map measures real space LDOS
  r(r,E)
• Fourier transformation of r(r,E)
• The FT of LDOS was first studied by Hoffman et
  al1.
• It was argued that the energy dependence of
  r(q,E) can be used to identify the ordering that
  breaks translational symmetry2.
• 1 J. E. Hoffman et al., Science 295, 466
  (2002).
• 2 D. Podolsky et al., Phys. Rev. B 67, 094514
  (2003).
• C. Howald et al., Phys. Rev. B 67, 014533
  (2003).

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STM results
Vershinin et al, Science Feb. 12 (2004).
cond-mat/0402320 Hanaguri et al, submitted to
Nature (2004) See also, J. E. Hoffman et al.,
Science 295, 466 (2002) and C. Howald et al.,
Phys. Rev. B 67, 014533 (2003).
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STM Theorems for the mean field BCS/pair density
wave state

• Assuming particle-hole symmetry and the pseudogap
  state being dominated by classical
  (time-independent) phase fluctuations, we show
  that
• for pair-density-wave with wavevector Q
• for charge-density-wave of holes with wavevector
  Q

Note particle-hole symmetry breaking does not
change the results qualitatively.
H.D. Chen, O. Vafek, A. Yazdani and S.C. Zhang,
cond-mat/0402323
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Energy dependence of ?(Q,E)
H.D. Chen, O. Vafek, A. Yazdani and S.C. Zhang,
cond-mat/0402323
9
Comparison with experiments

• Pair-density-wave is consistent with BSCCO
  experiments.
• The (2p/4.7a,0) peak picks up intensity when the
  pseudogap opens
• There is a p phase difference at high energy for
  atomic peaks and supermodulation peaks.
• There is no p phase difference at high energy for
  the new non-dispersive peak at (2p/4.5a,0)
• Pair-density-wave is consistent with recent NCCOC
  experiment.
• The periodicity of the new peak is commensurate
  4a x 4a, first predicted theoretically in H.D.
  Chen et al., Phys. Rev. Lett. 89 137004(2002).
• The (2p/4a,0) peak is even function of energy.
• The extra peak at (32p/4a,0) still needs to be
  understood.

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Comparison with experiments

• Pair-density-wave is consistent with BSCCO
  experiments.
• The (2p/4.7a,0) peak picks up intensity when the
  pseudogap opens
• There is a p phase difference at high energy for
  atomic peaks and supermodulation peaks.
• There is no p phase difference at high energy for
  the new non-dispersive peak at (2p/4.5a,0)
• Pair-density-wave is consistent with recent NCCOC
  experiment.
• The periodicity of the new peak is commensurate
  4a x 4a, first predicted theoretically in H.D.
  Chen et al., Phys. Rev. Lett. 89 137004(2002).
• The (2p/4a,0) peak is even function of energy.
• The extra peak at (32p/4a,0) still needs to be
  understood.

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Conclusion

• Hole pair crystal is a natural competing state to
  a superconductor with low superfluid density and
  short coherence length.
• For real doping x
• the periodicity of hole pair crystal is
• the periodicity of hole crystal is
• ?(Q,E) is even for pair-density-wave and odd for
  charge-density-wave of holes
• The width of (2p/4a,0) peak in Q-space increases
  as one moves away from the 1/8 filling.
• Pair-Density-Wave is consistent with STM
  experiments. STM can see the Cooper pairs
  directly!

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Conclusion

• Hole pair crystal is a natural competing state to
  a superconductor with low superfluid density and
  short coherence length.

• ?(Q,E) is even for pair-density-wave and odd for
  charge-density-wave of holes.

• The width of (2p/4a,0) peak in Q-space increases
  as one moves away from the 1/8 filling.

• Pair-Density-Wave is consistent with STM
  experiments. STM can see the Cooper pairs
  directly!