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Superconductivity from the `ordered’ limit. Jan Zaanen Zohar Nussinov Sergei Mukhin. Condensed Matter Physics Seminar John Hopkins University Baltimore, February 15th 2006. Vladimir Cvetković. Correlated superconductors. Ideal (Bose-Einstein) gas. BEC cold atomic gas,
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Superconductivity from the `ordered’ limit Jan Zaanen Zohar Nussinov Sergei Mukhin Condensed Matter Physics Seminar John Hopkins University Baltimore, February 15th 2006 Vladimir Cvetković
Correlatedsuperconductors Ideal (Bose-Einstein) gas BEC cold atomic gas, BCS superconductivity Helium 4 superfluid ω q Strongly correlated fluid
Correlatedsuperconductors Ideal (Bose-Einstein) gas BEC cold atomic gas, BCS superconductivity Helium 4 superfluid High Tc superconductors Strongly correlated fluid
Electrons comingto a standstill Electron crystals in cuprates Ca1.88Na0.12CuO2Cl2 Bi2Sr2CaCu2O8+d Bi2Sr2CaCu2O8+d Kapitulnik et al. 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’’ YB2Cu3O6.6 Bi2Sr2CaCu2O8+d YB2Cu3O6.6 Mook et al. Hoffman et al. Hinkov et al.
Correlatedsuperconductors Ideal (Bose-Einstein) gas BEC cold atomic gas, BCS superconductivity Helium 4 superfluid High Tc superconductors Strongly correlated fluid
Plan of talk • 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 • Liquid crystals • 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 • Liquid crystals • Duality (Higgs-Abelian) • Elasticity (quantum) • Elasticity + Duality • Charged nematic solid • Conclusions
2. XY dualityin 2+1D XY action Phase field: smooth and multivalued magnons vortices
2. XY dualityin 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 degreesof freedom I XY - Superfluid EM - Coulomb XY Magnon Transversal photon Coulomb interaction
Matching the degreesof freedom II XY - Mott insulator EM - Higgs Particle/hole Transversal photon Longitudinal photon Coulomb interaction VC, J. Zaanen, cond-mat/0511586; submitted to PRB
Plan of talk • Liquid crystals • Duality (Higgs-Abelian) • Elasticity (quantum) • Elasticity + Duality • Charged nematic solid • Conclusions
3. Elasticity –Strain action Displacement field Action Ideal crystal – two phonons • Longitudinal (compression + shear) • Transversal (shear) Phonon velocities
Displacementsingularities Dislocations Disclinations • Restores rotational • invariance • Destroys curvature • rigidity • Topological charge: • Franck scalar • Topological charge: • Burgers vector • Restores translational • invariance • Destroys shear rigidity
Find dislocations in electron DOS 1 2 3 4 1 5 2 6 3 7 8 4 5 6
Plan of talk • Liquid crystals • Duality (Higgs-Abelian) • Elasticity (quantum) • Elasticity + Duality • Charged nematic solid • 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 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 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 • Liquid crystals • Duality (Higgs-Abelian) • Elasticity (quantum) • Elasticity + Duality • Charged nematic solid • Conclusions
5. Addingelectric 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 energyloss 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 orderednematic 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 ℤ2 symmetry GLW action for (dislocation) loop gas Director order/disorder Ordered nematic -- U(1) gauge symmetry preserved