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Vladimir Cvetković

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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Vladimir Cvetković

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  1. Superconductivity from the `ordered’ limit Jan Zaanen Zohar Nussinov Sergei Mukhin Condensed Matter Physics Seminar John Hopkins University Baltimore, February 15th 2006 Vladimir Cvetković

  2. Correlatedsuperconductors Ideal (Bose-Einstein) gas BEC cold atomic gas, BCS superconductivity Helium 4 superfluid ω q Strongly correlated fluid

  3. Correlatedsuperconductors Ideal (Bose-Einstein) gas BEC cold atomic gas, BCS superconductivity Helium 4 superfluid High Tc superconductors Strongly correlated fluid

  4. Electrons comingto a standstill Electron crystals in cuprates Ca1.88Na0.12CuO2Cl2 Bi2Sr2CaCu2O8+d Bi2Sr2CaCu2O8+d Kapitulnik et al. Vershinin et al. Hanaguri et al.

  5. Quantum fluctuating stripe order Stripes: Theory: Zaanen & Gunnarson; Kivelson & Emery; Schultz Experiments: La1.75Ba0.25CuO4 Sr14Cu24O41 Tranquada & Yamada Abbamonte et al.

  6. Transient stripe order ``Melted stripes’’ YB2Cu3O6.6 Bi2Sr2CaCu2O8+d YB2Cu3O6.6 Mook et al. Hoffman et al. Hinkov et al.

  7. Correlatedsuperconductors Ideal (Bose-Einstein) gas BEC cold atomic gas, BCS superconductivity Helium 4 superfluid High Tc superconductors Strongly correlated fluid

  8. Plan of talk • Liquid crystals • Duality (Higgs-Abelian) • Elasticity (quantum) • Elasticity + Duality • Charged nematic solid • Conclusions

  9. 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!)

  10. Plan of talk • Liquid crystals • Duality (Higgs-Abelian) • Elasticity (quantum) • Elasticity + Duality • Charged nematic solid • Conclusions

  11. 1. Liquid crystals Phase diagram

  12. Quantum liquid crystals Stripe melting (Kivelson, Fradkin, Emery; Nature 393, 550 (1998)) Quantum fluctuations (doping) induced melting

  13. Plan of talk • Liquid crystals • Duality (Higgs-Abelian) • Elasticity (quantum) • Elasticity + Duality • Charged nematic solid • Conclusions

  14. 2. XY dualityin 2+1D XY action Phase field: smooth and multivalued magnons vortices

  15. 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)

  16. Matching the degreesof freedom I XY - Superfluid EM - Coulomb XY Magnon Transversal photon Coulomb interaction

  17. 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

  18. Plan of talk • Liquid crystals • Duality (Higgs-Abelian) • Elasticity (quantum) • Elasticity + Duality • Charged nematic solid • Conclusions

  19. 3. Elasticity –Strain action Displacement field Action Ideal crystal – two phonons • Longitudinal (compression + shear) • Transversal (shear) Phonon velocities

  20. Displacementsingularities Dislocations Disclinations • Restores rotational • invariance • Destroys curvature • rigidity • Topological charge: • Franck scalar • Topological charge: • Burgers vector • Restores translational • invariance • Destroys shear rigidity

  21. Find dislocations in electron DOS 1 2 3 4 1 5 2 6 3 7 8 4 5 6

  22. Plan of talk • Liquid crystals • Duality (Higgs-Abelian) • Elasticity (quantum) • Elasticity + Duality • Charged nematic solid • Conclusions

  23. 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

  24. Disorder field Director order parameter GLW action for Burgers vector (director) GLW action for (dislocation) loop gas Higgs mechanism for the elastic photons

  25. 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.

  26. 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

  27. Plan of talk • Liquid crystals • Duality (Higgs-Abelian) • Elasticity (quantum) • Elasticity + Duality • Charged nematic solid • Conclusions

  28. 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

  29. 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

  30. 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:

  31. 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)

  32. Detecting the dual `electric shear’ photon Old fashioned (Dresden EELS) New fashioned (Taiwanese RIXS) `Smart’ (Reflective EELS)

  33. 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!)

  34. Charged orderednematic phase Anisotropic Extreme superconducting anisotropy Anisotropic effective `glide’ length Dynamical coupling between the magnetic and electric sectors: polaritons `visible’ in EELS

  35. Alternative description Burgers disorder fields ℤ2 symmetry GLW action for (dislocation) loop gas Director order/disorder Ordered nematic -- U(1) gauge symmetry preserved

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