Download `ordered` limit

Superconductivity from the
`ordered’ limit
Vladimir Cvetković
Jan Zaanen
Zohar Nussinov
Sergei Mukhin
Condensed Matter Physics Seminar
John Hopkins University
Baltimore, February 15th 2006
Correlated
superconductors
Ideal (Bose-Einstein) gas
BEC cold atomic gas,
BCS superconductivity
Helium 4 superfluid
ω
q
Strongly correlated fluid
Correlated
superconductors
Ideal (Bose-Einstein) gas
BEC cold atomic gas,
BCS superconductivity
Helium 4 superfluid
High Tc superconductors
Strongly correlated fluid
Electrons coming
to a standstill
Electron crystals in cuprates
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Bi2Sr2CaCu2O8+d
Kapitulnik et al.
Bi2Sr2CaCu2O8+d
Ca1.88Na0.12CuO2Cl2
Vershinin et al.
Hanaguri et al.
Quantum fluctuating
stripe order
Stripes:
Theory: Zaanen & Gunnarson; Kivelson & Emery; Schultz
Experiments:
La1.75Ba0.25CuO4
Sr14Cu24O41
Tranquada & Yamada
Abbamonte et al.
Transient stripe order
``Melted stripes’’
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YB2Cu3O6.6
Bi2Sr2CaCu2O8+d
YB2Cu3O6.6
Mook et al.
Hoffman et al.
Hinkov et al.
Correlated
superconductors
Ideal (Bose-Einstein) gas
BEC cold atomic gas,
BCS superconductivity
Helium 4 superfluid
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High Tc superconductors
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Strongly correlated fluid
Plan of talk
1.
2.
3.
4.
5.
6.
Liquid crystals
Duality (Higgs-Abelian)
Elasticity (quantum)
Elasticity + Duality
Charged nematic solid
Conclusions
Conclusions
•Dislocation mediated melting of a
neutral / Wigner / stripe crystal
•Superconducting state
•Unconventional magnetic screening -- oscillating
screening currents
•Unconventional electric screening -- overscreening
of the Coulomb potential
•New pole(s) in the electron energy loss function as
a signature of new (superconducting) phase
(experimentally accessible!)
Plan of talk
1. Liquid crystals
2.
3.
4.
5.
6.
Duality (Higgs-Abelian)
Elasticity (quantum)
Elasticity + Duality
Charged nematic solid
Conclusions
1. Liquid crystals
Phase diagram
Quantum liquid crystals
Stripe melting (Kivelson, Fradkin, Emery; Nature 393, 550 (1998))
Quantum fluctuations (doping) induced melting
Plan of talk
1. Liquid crystals
2. Duality (Higgs-Abelian)
3.
4.
5.
6.
Elasticity (quantum)
Elasticity + Duality
Charged nematic solid
Conclusions
2. XY duality
in 2+1D
XY action
Phase field:
smooth and multivalued
magnons
vortices
2. XY duality
in 2+1D
XY action
Conjugated momentum
Gauge fields
Currents
EM action with
vortices as charges
XY
Superfluid
Mott insulator
EM
Coulomb
Superconductor
(Higgs)
Matching the degrees
of freedom I
XY - Superfluid
XY Magnon
EM - Coulomb
Transversal photon
Coulomb interaction
Matching the degrees
of freedom II
XY - Mott insulator
Particle/hole
EM - Higgs
Transversal photon
Longitudinal photon
Coulomb interaction
VC, J. Zaanen, cond-mat/0511586; submitted to PRB
Plan of talk
1. Liquid crystals
2. Duality (Higgs-Abelian)
3. Elasticity (quantum)
4. Elasticity + Duality
5. Charged nematic solid
6. Conclusions
3. Elasticity –
Strain action
Displacement field
Action
Ideal crystal – two phonons
• Longitudinal (compression + shear)
• Transversal (shear)
Phonon velocities
Displacement
singularities
Dislocations
•Topological charge:
Burgers vector
•Restores translational
invariance
•Destroys shear rigidity
Disclinations
•Restores rotational
invariance
•Destroys curvature
rigidity
•Topological charge:
Franck scalar
Find dislocations in
electron DOS
1
2
3
1
4
2
3
4
5
6
5
6
7
8
Plan of talk
1. Liquid crystals
2. Duality (Higgs-Abelian)
3. Elasticity (quantum)
4. Elasticity + Duality
5. Charged nematic solid
6. Conclusions
4. Duality +
Elasticity
Stress field
Dual stress gauge fields
Dislocation currents
Our dual action
Angular conservation -- Ehrenfest constraint
Three degrees of freedom
Two phonons (photons)
+ `Coulomb’ interaction
Disorder field
Director order parameter
Q ab  n a n b  12 d ab
GLW action for Burgers vector (director)
GLW action for (dislocation) loop gas
Higgs mechanism for the elastic photons
Dislocation kinetics
Glide
Climb
Allowed – reconnecting
Disallowed – excess material
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Climb makes the compression stress short-ranged!
VC, Z. Nussinov, J. Zaanen, cond-mat/0508664, to appear in Phil. Mag.
Neutral nematic crystal
The nematic phase = the `dual’ shear superconductor
Longitudinal
Transversal
ω
ω
q
q
J. Zaanen et al., Ann.Phys. 310, 181 (2004);
VC, J. Zaanen, Z. Nussinov, S. Mukhin, in preparation
Plan of talk
1.
2.
3.
4.
Liquid crystals
Duality (Higgs-Abelian)
Elasticity (quantum)
Elasticity + Duality
5. Charged nematic solid
6. Conclusions
5. Adding
electric charge
Charged particles – Wigner crystal
Extra terms in the dual action
• Dual stress to EM gauge fields coupling
• Bare Meissner
Charged crystal innate superconductor but...
... dual stress gauge fields dress it back
Static magnetic
screening
Dual shear superconductor: bare Meissner liberated
Static screening (Meissner)
Characteristic screening lengths
•London (magnetic)
•Shear
Screening type
•Normal (conventional SC) at 2λL > λS
•Oscillating currents at 2λL < λS
Static Coulomb
screening
Static Coulomb term
Characteristic screening lengths
•Ideal crystal screening length
•Liquid screening length
•Dislocation correlation length
Coulomb potential screened
in all phases
•Disorder lines
Physically relevant regime:
Electron energy
loss function
Electric permeability
(dynamical Coulomb propagator)
Energy loss function
Gap values:
Extra pole in the electron loss function!
VC, J. Zaanen, Z. Nussinov,
S. Mukhin, in preparation (2)
Detecting the dual
`electric shear’ photon
Old fashioned
(Dresden EELS)
New fashioned
(Taiwanese RIXS)
`Smart’
(Reflective EELS)
Conclusions
•Dislocation mediated melting of a
neutral / Wigner / stripe crystal
•Superconducting state
•Unconventional magnetic screening -- oscillating
screening currents
•Unconventional electric screening -- overscreening
of the Coulomb potential
•New pole(s) in the electron energy loss function as
a signature of new (superconducting) phase
(experimentally accessible!)
Charged ordered
nematic phase
Anisotropic
Extreme superconducting
anisotropy
Anisotropic effective
`glide’ length
Dynamical coupling between the
magnetic and electric sectors:
polaritons `visible’ in EELS
Alternative description
Burgers disorder fields
b
Jb  Jb
ℤ2 symmetry
GLW action for (dislocation)
loop gas

2
2

a a
2
1
Sdis  2  d  d x db
  ib B  b  m 
b 

 
b  b
 db' 
2
b
Vb b'  b'
Director order/disorder
Qab  Qab b ,b 
Ordered nematic -- U(1) gauge symmetry preserved

2


