High Tc Superconductors

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High Tc Superconductors QED3 theory of the
cuprates

• Tami Pereg-Barnea
• UBC
• tami_at_physics.ubc.ca

QED3
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outline

• High Tc Known and unknown
• Some experimental facts and phenomenology
• Models
• Attempts to solve the problem
• The inverted approach
• QED3 formulations and consequences

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Facts

• The parent compounds are AF insulators.
• 2D layers of CuO2
• Superconductivity is the condensation of Cupper
  pairs with a D-wave pairing potential.
• The cuprates are superconductors of type II
• The normal state is a non-Fermi liquid,
  strange metal.

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YBCO microwave conductivity
BSCCOARPES
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Neutron scattering (p,p) resonance in YBCO
Underdoped Bi2212
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Phenomenology

• The superconducting state is a D-wave BCS
  superconductors with a Fermi liquid of nodal
  quasiparticles.
• The AF state is well described by a Mott-Hubbard
  model with large U repulsion.
• The pseudogap is strange!
• Gap in the excitation of D-wave symmetry but no
  superconductivity
• Non Fermi liquid behaviour anomalous power laws
  in verious observables.

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Phase diagram
AF
AF
AF
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Theoretical approaches

• Starting from the Hubbard model at ½ filling.
• Slave bosons SU(2) gauge theories
• Spin and charge separation
• Stripes
• Phenomenological
• SO(5) theory
• DDW competing order

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The inverted approach

• Use the phenomenology of d-SC as a starting
  point.
• Destroy superconductivity without closing the
  gap and march backwards along the doping axis.
• The superconductivity is lost due to
  quantum/thermal fluctuations in the phase of the
  order parameter.

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Vortex Antivortex unbinding
Emery Kivelson Nature 374, 434 (1995) Franz
Millis PRB 58, 14572 (1998)
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Phase fluctuations

• Assume D0 D const.
• Treat expif(r) as a quantum number sum over
  all paths.
• Fluctuations in f are smooth (spin waves) or
  singular (vortices).
• Perform the Franz Teanovic transformation - a
  singular gauge transformation.
• The phase information is encoded in the dressed
  fermions and two new gauge fields.

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Formalism

• Start with the BdG Hamiltonian
• FT transformation in order to avoid branch cuts.

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The transformed Hamiltonian

• The gauge field am couples minimally ?m ? am
• The resulting partition function is averaged over
  all A, B configurations and the two gauge fields
  are coarse grained.

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The physical picture

• RG arguments show that vm is massive and
  therefore its interaction with the Toplogical
  fermions is irrelevant.
• The am field is massive in the dSC phase
  (irrelevant at low E) and massless at the
  pseudogap.
• The kinetic energy of am is Maxwell - like.

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Quantum Electro Dynamics

• Linearization of the theory around the nodes.
• Construction of 2 4-component Dirac spinors.

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Dressed QPs
Optimally doped BSCCO Above Tc T.Valla et al.
PRL (00)
QED3 Spectral function
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Chiral Symmetry Breaking ? AF order

• The theory of Quantum electro dynamics has an
  additional symmetry, that does not exist in the
  original theory.
• The Lagrangian is invariant under the global
  transformation where G is a linear
  combination of

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• The symmetry is broken spontaneously through the
  interaction of the fermions and the gauge field.
• The symmetry breaking (mass) terms that are added
  to the action, written in the original nodal QP
  operators represent
• Subdominant dis SC order parameter
• Subdominant dip SC order parameter
• Charge density waves
• Spin density waves

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Antiferromagnetism

• The spin density wave is described by
  
• where ?, ? labels denote nodes.
• The momentum transfer is Q, which spans two
  antipodal nodes.
• At ½ filling, Q ? (?,?) commensurate
  Antiferromagnetism.

_
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Summary

• Inverted approach dSC ? PSG ? AF
• View the pseudogap as a phase disordered
  superconductor.
• Use a singular gauge transformation to encode the
  phase fluctuation in a gauge field and get QED3
  effective theory.
• Chirally symmetric QED3 ? Pseudogap
• Broken symmetry ? Antiferromagnetism