Quantum criticality in the

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Quantum criticality in the cuprate
superconductors Talk online
sachdev.physics.harvard.edu
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Outline
1. Quantum criticality Coupled dimer
antiferromagnets vs. the
cuprate superconductors 2. Fermi surfaces in
the hole-doped cuprates Observations of
quantum oscillations 3. Superconductivity
4. Competition between spin-density-wave
order and superconductivity
phenomenological theory 5. Electronic theory of
superconductivity and its competition with
spin-density-wave order
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Quantum criticality coupled dimer
antiferromagets vs. the cuprate supercondcutors
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Square lattice antiferromagnet
Ground state has long-range Néel order
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Square lattice antiferromagnet
J
J/
Weaken some bonds to induce spin entanglement in
a new quantum phase
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Square lattice antiferromagnet
J
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Ground state is a quantum paramagnet with spins
locked in valence bond singlets
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R. A. Cooper, Y. Wang, B. Vignolle, O. J.
Lipscombe, S. M. Hayden, Y. Tanabe, T. Adachi, Y.
Koike, M. Nohara, H. Takagi, Cyril Proust, N. E.
Hussey, Science, 323, 603 (2009).
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Crossovers in transport properties of hole-doped
cuprates
N. E. Hussey, J. Phys Condens. Matter 20,
123201 (2008)
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Only candidate quantum critical point observed at
low T
Strange metal
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Fermi surfaces in the hole-doped cuprates
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Spin density wave theory
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Theory of quantum criticality in the cuprates
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Quantum oscillations
N. Doiron-Leyraud, C. Proust, D. LeBoeuf, J.
Levallois, J.-B. Bonnemaison, R. Liang,
D. A. Bonn, W. N. Hardy, and L. Taillefer,
Nature 447, 565 (2007)
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Quantum oscillations
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Quantum oscillations
Nature 450, 533 (2007)
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Quantum oscillations
Nature 450, 533 (2007)
Quantum oscillations can be explained by SDW
theory, but electron pockets are not seen in
photoemission. Clear hole pockets are not seen
either.
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Superconductivity in hole-doped cuprates
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Theory of quantum criticality in the cuprates
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Theory of quantum criticality in the cuprates
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Competition between SDW order and
superconductivity phenomenological theory
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Phenomenological quantum theory of competition
between superconductivity (SC) and spin-density
wave (SDW) order
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Phenomenological quantum theory of competition
between superconductivity (SC) and spin-density
wave (SDW) order
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Phenomenological quantum theory of competition
between superconductivity (SC) and spin-density
wave (SDW) order
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Phenomenological quantum theory of competition
between superconductivity (SC) and spin-density
wave (SDW) order
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J. Chang, Ch. Niedermayer, R. Gilardi, N.B.
Christensen, H.M. Ronnow, D.F. McMorrow, M. Ay,
J. Stahn, O. Sobolev, A. Hiess, S. Pailhes, C.
Baines, N. Momono, M. Oda, M. Ido, and J.
Mesot, Physical Review B 78, 104525 (2008).
J. Chang, N. B. Christensen, Ch.
Niedermayer, K. Lefmann, H. M. Roennow, D.
F. McMorrow, A. Schneidewind, P. Link, A.
Hiess, M. Boehm, R. Mottl, S. Pailhes, N.
Momono, M. Oda, M. Ido, and J. Mesot, Phys. Rev.
Lett. 102, 177006 (2009).
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D. Haug, V. Hinkov, A. Suchaneck, D. S. Inosov,
N. B. Christensen, Ch. Niedermayer, P. Bourges,
Y. Sidis, J. T. Park, A. Ivanov, C. T. Lin, J.
Mesot, and B. Keimer, arXiv0902.3335.
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Electronic theory of superconductivity and its
competition with spin-density wave order
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Theory of quantum criticality in the cuprates
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Theory of quantum criticality in the cuprates
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Pairing by SDW fluctuation exchange
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Approaching the onset of antiferromagnetism in
the spin-fluctuation theory
Ar. Abanov, A. V. Chubukov and J. Schmalian,
Advances in Physics 52, 119 (2003).
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Approaching the onset of antiferromagnetism in
the spin-fluctuation theory
Ar. Abanov, A. V. Chubukov and J. Schmalian,
Advances in Physics 52, 119 (2003).
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Theory of quantum criticality in the cuprates
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Conclusions
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Crossovers in transport properties of hole-doped
cuprates
N. E. Hussey, J. Phys Condens. Matter 20,
123201 (2008)
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Only candidate quantum critical point observed at
low T
Strange metal
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Theory of quantum criticality in the cuprates
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Conclusions

• Gauge theory for pairing in the underdoped
  cuprates, describing angular fluctuations of
  spin-density-wave order
• Natural route to d-wave pairing with strong
  pairing at the antinodes and weak pairing at the
  nodes
• Explains characteristic competing order
  features of field-doping phase diagram SDW order
  is more stable in the metal than in the
  superconductor.