Subir Sachdev

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Loss of Neel order in insulators and
superconductors
Cenke Xu
Ribhu Kaul
Max Metlitski
Subir Sachdev arXiv0804.1794
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Phase diagram of electron-doped superconductors
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Spin correlations in the electron-doped
high-transition-temperature superconductor
Nd2-xCexCuO4 E. M. Motoyama, G. Yu, I. M. Vishik,
O. P. Vajk, P. K. Mang and M. Greven Nature 445,
186-189(11 January 2007)
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Photoemission in NCCO
N. P. Armitage et al., Phys. Rev. Lett. 88,
257001 (2002).
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Nature 450, 533 (2007)
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Outline
1. Loss of Neel order in insulating square
lattice antiferromagnets
Distinct universality classes for half-integer,
odd integer, and even integer spin
S 2. Low energy theory for doped S1/2
antiferromagnets d-wave superconductivity 3.
Loss of Neel order in the d-wave superconductor
Same universality classes as in general S
insulators, leading to transitions
to a valence bond supersolid, a
nematic superconductor, or a vanilla
superconductor
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Outline
1. Loss of Neel order in insulating square
lattice antiferromagnets
Distinct universality classes for half-integer,
odd integer, and even integer spin
S 2. Low energy theory for doped S1/2
antiferromagnets d-wave superconductivity 3.
Loss of Neel order in the d-wave superconductor
Same universality classes as in general S
insulators, leading to transitions
to a valence bond supersolid, a
nematic superconductor, or a vanilla
superconductor
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Coupled dimer antiferromagnet
M. Matsumoto, C. Yasuda, S. Todo, and H.
Takayama, Phys. Rev.B 65, 014407 (2002).
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Square lattice antiferromagnet
Ground state has long-range Néel order
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Square lattice antiferromagnet
Destroy Neel order by perturbations which
preserve full square lattice symmetry e.g.
second-neighbor or ring exchange.
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Square lattice antiferromagnet
Destroy Neel order by perturbations which
preserve full square lattice symmetry e.g.
second-neighbor or ring exchange.
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Theory for loss of Neel order
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Perturbation theory
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Perturbation theory
Distinct universality from O(3) model
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Non-perturbative effects
F. D. M. Haldane, Phys. Rev. Lett. 61, 1029
(1988).
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Half-odd-integer S
Loss of Neel order leads to a Valence Bond Solid
(VBS)
N. Read and S. Sachdev, Phys. Rev. Lett. 62, 1694
(1989).
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Odd integer S
Loss of Neel order leads to a (charge) nematic
N. Read and S. Sachdev, Phys. Rev. Lett. 62, 1694
(1989).
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Even integer S
Loss of Neel order leads to a state with no
broken symmetry
N. Read and S. Sachdev, Phys. Rev. Lett. 62, 1694
(1989).
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Outline
1. Loss of Neel order in insulating square
lattice antiferromagnets
Distinct universality classes for half-integer,
odd integer, and even integer spin
S 2. Low energy theory for doped S1/2
antiferromagnets d-wave superconductivity 3.
Loss of Neel order in the d-wave superconductor
Same universality classes as in general S
insulators, leading to transitions
to a valence bond supersolid, a
nematic superconductor, or a vanilla
superconductor
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Outline
1. Loss of Neel order in insulating square
lattice antiferromagnets
Distinct universality classes for half-integer,
odd integer, and even integer spin
S 2. Low energy theory for doped S1/2
antiferromagnets d-wave superconductivity 3.
Loss of Neel order in the d-wave superconductor
Same universality classes as in general S
insulators, leading to transitions
to a valence bond supersolid, a
nematic superconductor, or a vanilla
superconductor
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Hole dynamics in an antiferromagnet across a
deconfined quantum critical point, R. K. Kaul,
A. Kolezhuk, M. Levin, S. Sachdev, and T.
Senthil, Physical Review B 75 , 235122 (2007).
Algebraic charge liquids and the underdoped
cuprates, R. K. Kaul, Y. B. Kim, S. Sachdev, and
T. Senthil, Nature Physics 4, 28 (2008).
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Conventional phases
AF Metal
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Conventional phases
AF d-wave superconductor
4 Dirac points ( 4 shadows)
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Conventional phases
AF d-wave superconductor
Fermions fully gapped
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Outline
1. Loss of Neel order in insulating square
lattice antiferromagnets
Distinct universality classes for half-integer,
odd integer, and even integer spin
S 2. Low energy theory for doped S1/2
antiferromagnets d-wave superconductivity 3.
Loss of Neel order in the d-wave superconductor
Same universality classes as in general S
insulators, leading to transitions
to a valence bond supersolid, a
nematic superconductor, or a vanilla
superconductor
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Outline
1. Loss of Neel order in insulating square
lattice antiferromagnets
Distinct universality classes for half-integer,
odd integer, and even integer spin
S 2. Low energy theory for doped S1/2
antiferromagnets d-wave superconductivity 3.
Loss of Neel order in the d-wave superconductor
Same universality classes as in general S
insulators, leading to transitions
to a valence bond supersolid, a
nematic superconductor, or a vanilla
superconductor
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Loss of Neel order in AFM d-wave superconductor
Fermions fully gapped
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Perturbation theory
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Recall non-perturbative effects in insulator
F. D. M. Haldane, Phys. Rev. Lett. 61, 1029
(1988).
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Non-perturbative effects in superconductor
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Non-perturbative effects in superconductor
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Non-perturbative effects in superconductor
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Non-perturbative effects in superconductor
Transitions match those found in insulators for
different S
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Loss of Neel order in AFM d-wave superconductor
with gapless fermions
4 Dirac points ( 4 shadows)
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Perturbation theory
R. K. Kaul, Y. B. Kim, S. Sachdev, and T.
Senthil, Nature Physics 4, 28 (2008)
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Non-perturbative effects in superconductor
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Conclusions

• Theory for the loss of Neel order in d-wave
  superconductors
• For superconductors with gapped Bogoliubov
  quasiparticles, we found 3 distinct transitions,
  to a valence bond supersolid, a nematic
  superconductor, and a vanilla superconductor
• These transitions in the compressible
  superconductor of S1/2 electrons match the
  classification of transitions in the
  incompressible Mott insulator of general S spins.