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