Post on 23-Jan-2016
description
Vladimir CvetkovićJan Zaanen
Zohar Nussinov Sergei Mukhin
Condensed Matter Physics SeminarJohn Hopkins University
Baltimore, February 15th 2006
Superconductivity from the `ordered’ limit
Correlatedsuperconductors
Ideal (Bose-Einstein) gas
Strongly correlated fluid
BEC cold atomic gas,BCS superconductivity
Helium 4 superfluid ω
q
Correlatedsuperconductors
Ideal (Bose-Einstein) gas
Strongly correlated fluid
BEC cold atomic gas,BCS superconductivity
Helium 4 superfluid
High Tc superconductors
Electrons comingto a standstill
Electron crystals in cuprates
Bi2Sr2CaCu2O8+Ca1.88Na0.12CuO2Cl2
Hanaguri et al.Kapitulnik et al.
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Vershinin et al.
Bi2Sr2CaCu2O8+
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’’
Bi2Sr2CaCu2O8+
Hoffman et al.
YB2Cu3O6.6
Mook et al.
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Hinkov et al.
YB2Cu3O6.6
Correlatedsuperconductors
Ideal (Bose-Einstein) gas
Strongly correlated fluid
BEC cold atomic gas,BCS superconductivity
Helium 4 superfluid
High Tc superconductors
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Plan of talk
1. Liquid crystals2. Duality (Higgs-Abelian)3. Elasticity (quantum)4. Elasticity + Duality5. Charged nematic solid6. Conclusions
Conclusions
•Dislocation mediated melting of aneutral / Wigner / stripe crystal
•Superconducting state
•Unconventional magnetic screening -- oscillating screening currents
•Unconventional electric screening -- overscreeningof the Coulomb potential
•New pole(s) in the electron energy loss function asa signature of new (superconducting) phase(experimentally accessible!)
Plan of talk
1. Liquid crystals2. Duality (Higgs-Abelian)3. Elasticity (quantum)4. Elasticity + Duality5. Charged nematic solid6. Conclusions
1. Liquid crystals
Phase diagram
Quantum liquid crystals
Quantum fluctuations (doping) induced melting
Stripe melting (Kivelson, Fradkin, Emery; Nature 393, 550
(1998))
Plan of talk
1. Liquid crystals
2. Duality (Higgs-Abelian)3. Elasticity (quantum)4. Elasticity + Duality5. Charged nematic solid6. Conclusions
2. XY dualityin 2+1D
XY action
Phase field:smooth and multivalued
vorticesmagnons
2. XY dualityin 2+1D
XY action
Superfluid Mott insulatorXY
Coulomb Superconductor(Higgs)
EM
Conjugated momentum
Gauge fields
Currents
EM action withvortices as charges
Matching the degrees
of freedom IXY - Superfluid
Transversal photon
EM - Coulomb
Coulomb interaction
XY Magnon
Matching the degrees
of freedom IIXY - Mott insulator EM - Higgs
Particle/hole Transversal photon
Coulomb interaction
Longitudinal photon
VC, J. Zaanen, cond-mat/0511586; submitted to PRB
Plan of talk
1. Liquid crystals2. Duality (Higgs-Abelian)
3. Elasticity (quantum)4. Elasticity + Duality5. Charged nematic solid6. Conclusions
3. Elasticity –Strain action
Displacement field
Action
• Longitudinal (compression + shear)• Transversal (shear)
Ideal crystal – two phonons
Phonon velocities
Displacementsingularities
Dislocations Disclinations
•Destroys shear rigidity
•Restores rotationalinvariance
•Destroys curvaturerigidity
•Topological charge:Franck scalar
•Topological charge:Burgers vector
•Restores translationalinvariance
Find dislocations in electron DOS
12
34
56
78
12
45
6
3
Plan of talk
1. Liquid crystals2. Duality (Higgs-Abelian)3. Elasticity (quantum)
4. Elasticity + Duality5. Charged nematic solid6. Conclusions
4. Duality +Elasticity
Stress field
Dual stress gauge fields
Our dual action
Dislocation currents
Angular conservation -- Ehrenfest constraint
Three degrees of freedom
Two phonons (photons) + `Coulomb’ interaction
Disorder field
Director order parameter abbaab nnQ 21−=
GLW action for Burgers vector (director)
GLW action for (dislocation) loop gas
Higgs mechanism for the elastic photons
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Dislocation kinetics
Glide ClimbAllowed – reconnecting Disallowed – excess material
Climb makes the compression stress short-ranged!
VC, Z. Nussinov, J. Zaanen, cond-mat/0508664, to appear in Phil. Mag.
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Neutral nematic crystal
The nematic phase = the `dual’ shear superconductorLongitudinal Transversal
ω ω
q qJ. Zaanen et al., Ann.Phys. 310, 181 (2004);VC, J. Zaanen, Z. Nussinov, S. Mukhin, in preparation
Plan of talk
1. Liquid crystals2. Duality (Higgs-Abelian)3. Elasticity (quantum)4. Elasticity + Duality
5. Charged nematic solid6. Conclusions
5. Addingelectric charge
Charged particles – Wigner crystal
Extra terms in the dual action
Charged crystal innate superconductor but...
... dual stress gauge fields dress it back
• Dual stress to EM gauge fields coupling
• Bare Meissner
Static magnetic screening
Characteristic screening lengths
•London (magnetic)
•Shear
Static screening (Meissner)
Screening type
•Normal (conventional SC) at 2λL > λS
•Oscillating currents at 2λL < λS
Dual shear superconductor: bare Meissner liberated
Static Coulomb screening
Characteristic screening lengths•Ideal crystal screening length
•Liquid screening length
•Dislocation correlation length
Static Coulomb term
Coulomb potential screenedin all phases
•Disorder lines
Physically relevant regime:
Electron energyloss function
Electric permeability(dynamical Coulomb propagator)
Extra pole in the electron loss function!
Energy loss function
Gap values:
VC, J. Zaanen, Z. Nussinov,S. Mukhin, in preparation (2)
Detecting the dual `electric shear’
photonOld fashioned
(Dresden EELS)New fashioned
(Taiwanese RIXS)`Smart’
(Reflective EELS)
Conclusions
•Dislocation mediated melting of aneutral / Wigner / stripe crystal
•Superconducting state
•Unconventional magnetic screening -- oscillating screening currents
•Unconventional electric screening -- overscreeningof the Coulomb potential
•New pole(s) in the electron energy loss function asa signature of new (superconducting) phase(experimentally accessible!)
Charged orderednematic phase
Anisotropic
Anisotropic effective`glide’ length
Dynamical coupling between themagnetic and electric sectors:polaritons `visible’ in EELS
Extreme superconductinganisotropy
Alternative description
Burgers disorder fields
€
ψb
ℤ2 symmetry
€
Sdis = 12 dτ dxdb∫ ∂μ − ibaBμ
a( )ψ b
2+ m2 ψ b
2+ db'ψ b
2Vb⋅b'ψ b '
2∫ ⎡ ⎣ ⎢
⎤ ⎦ ⎥
GLW action for (dislocation) loop gas
Director order/disorder
€
Qab = Qab ψ b ,ψ b( )
€
ψ−b =ψ b
Ordered nematic -- U(1) gauge symmetry preserved
€
Jμ−b = −Jμ
b