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Vortex drag in a Thin-film Giaever transformer

Vortex drag in a Thin-film Giaever transformer. Yue (Rick) Zou (Caltech) Gil Refael (Caltech) Jongsoo Yoon (UVA) Past collaboration: Victor Galitski (UMD) Matthew Fisher (Caltech) T. Senthil (MIT). $$$: Research corporation, Packard Foundation, Sloan Foundation. Outline.

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Vortex drag in a Thin-film Giaever transformer

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  1. Vortex drag in a Thin-film Giaever transformer Yue (Rick) Zou (Caltech) Gil Refael (Caltech) Jongsoo Yoon (UVA) Past collaboration: Victor Galitski (UMD) Matthew Fisher (Caltech) T. Senthil (MIT) $$$: Research corporation, Packard Foundation, Sloan Foundation

  2. Outline • Experimental Motivation – SC-metal-insulator in InO, TiN, Ta and MoGe. • Two paradigms: • - Vortex condensation: Vortex metal theory. • - Percolation paradigm • Thin film Giaever transformer – amorphous thin-film bilayer. • Predictions for the no-tunneling regime of a thin-film bilayer • Conclusions

  3. I Quantum vortex physics SC-insulator transition • Thin films: B tunes a SC-Insulator transition. V InO Ins B B (Hebard, Paalanen, PRL 1990) SC

  4. Saturation as T 0 Observation of Superconductor-insulator transition • Thin amorphous films: B tunes a SC-Insulator transition. InO: (Sambandamurthy, Engel, Johansson, Shahar, PRL 2004) (Steiner, Kapitulnik) • Insulating peak different from sample to sample, scaling different – log, activated.

  5. Observation of a metallic phase • MoGe: (Mason, Kapitulnik, PRB 1999)

  6. Observation of a metallic phase • Ta: (Qin, Vicente, Yoon, 2006) • Saturation at ~100mK: New metalic phase? (or saturation of electrons temperature)

  7. Vortex Paradigm

  8. Correlated states in higher dimensions: Superconductivity • Pairs of electrons form Cooper pairs: (c’s are creation operators for electrons) • Cooper pairs are bosons, and can Bose-Einstein condense: Meissner effect H. K. Onnes, Commun. Phys. Lab.12,120, (1911) Gap in tunneling density of states www.egglescliffe.org.uk http://dept.phy.bme.hu/research/sollab_nano.html

  9. Supercurrent: • Vortices: (Josephson I) • Vortex motion leads to a voltage drop: V (Josephson II) Free energy of a superconductor – Landau-Ginzburg theory • Most interesting, phase dynamics .

  10. Charging energy: Hopping: • Large U - Mott insulator (no charge fluctuations) • Large - Superfluid (intense charge fluctuations, no phase fluctuations) insulator superfluid X-Y model for superconducting film: Cooper pairs as Bosons • When the superconducting order is strong – ignore electronic excitations. • Standard model for bosonic SF-Ins transition – “Bose-Hubbard model”:

  11. Vortex: Cooper-pairs: • Vortex-vortex interactions: superfluid insulator Vortices: V-superfluid V- insulator Vortex description of the SF-insulator transition (Fisher, 1990) • Vortex hopping: (result of charging effects) Condensed vortices = insulating CP’s

  12. In reality superconducting films are not self dual: • vortices interact logarithmically, Cooper-pairs interact at most with power law. • Samples are very disordered and the disorder is different for cooper-pairs and vortices. • Current due to CP hopping: 2e • EMF due to vortex hopping: • Resistance: Universal (?) resistance at SF-insulator transition Assume that vortices and Cooper-pairs are self dual at transition point.

  13. Net vortex density: Magnetically tuned Superconductor-insulator transition • Disorder pins vortices for small field – superconducting phase. • Large fields some free vortices appear and condense – insulating phase. • Larger fields superconductivity is destroyed – normal (unpaired) phase. Disorder pins vortices: Free vortices: Vortex SF insulator Disorder localized Electrons: Normal (unpaired) Phase coherent SC

  14. Metallic phase? Magnetically tuned Superconductor-insulator transition • Net vortex density: Problems • Saturation of the resistance – ‘metallic phase’ • Non-universal insulating peak – completely different depending on disorder. Disorder localized Electrons: Normal (unpaired)

  15. Disorder induced Gapless QP’s (electron channel) Uncondensed vortices: Cooper-pair channel (delocalized core states?) Finite conductivity: Two-fluid model for the SC-Metal-Insulator transition (Galitski, Refael, Fisher, Senthil, 2005) Two channels in parallel:

  16. Assume: • - grows from zero to . - grows from zero to infinity. B B Weak insulators: Ta, MoGe Weak InO B Transport properties of the vortex-metal Effective conductivity: Vortex metal Normal (unpaired)

  17. Assume: • - grows from zero to . - grows from zero to infinity. B B Strong insulators: TiN, InO B Transport properties of the vortex-metal Effective conductivity: Chargless spinons contribute to conductivity! Vortex metal Insulator Normal (unpaired)

  18. More physical properties of the vortex metal • A superconducting STM can tunnel Cooper pairs to the film: (Naaman, Tyzer, Dynes, 2001). Cooper pair tunneling

  19. More physical properties of the vortex metal CP CP Vortex metal e e Insulator Normal (unpaired) strongly T dependent B Cooper pair tunneling • A superconducting STM can tunnel Cooper pairs to the film: Vortex metal phase: Normal phase:

  20. Percolation Paradigm (Trivedi, Dubi, Meir,Avishai, Spivak, Kivelson,et al.)

  21. Pardigm II: superconducting vs. Normal regions percolation SC NOR NOR R B • Strong disorder breaks the film into superconducting and normal regions.

  22. NOR Pardigm II: superconducting vs. Normal regions percolation • Strong disorder breaks the film into superconducting and normal regions. SC SC SC SC SC R B • Near percolation – thin channels of the disorder-localized normal phase.

  23. NOR Pardigm II: superconducting vs. Normal regions percolation • Strong disorder breaks the film into superconducting and normal regions. R B • Near percolation – thin channels of the disorder-localized normal phase. • Far from percolation – normal electrons with disorder.

  24. NOR island SC island Nor-SC links: SC-SC links: Normal links: Magneto-resistance curves in the percolation picture (Dubi, Meir, Avishai, 2006) • Simulate film as a resistor network: Reuslting MR:

  25. Drag in a bilayer system

  26. Giaever transformer – Vortex drag B B Vortices tightly bound: (Giaever, 1965) Two type-II bulk superconductors:

  27. 2DEG bilayers – Coulomb drag Two thin electron gases: • Coulomb force creates friction between the layers. • Inversely proportional to density squared: • Opposite sign to Giaever’s vortex drag.

  28. 2DEG bilayers – Coulomb drag “Excitonic condensate” (Kellogg, Eisenstein, Pfeiffer, West, 2002) Two thin electron gases: Example:

  29. Percolation paradigm Vortex condensation paradigm • Electron density: • Vortex density: ) ( QH bilayers: Thin film Giaever transformer Insulating layer, Josephson tunneling: Amorphous (SC) thin films or • Drag is due to inductive current interactions, and Josephson coupling. • Drag is due to coulomb interaction. ? Drag suppressed Significant Drag

  30. ?

  31. Vortex drag in thin films bilayers: interlayer interaction e.g., Pearl penetration length: • Vortex current suppressed. r • Vortex attraction=interlayer induction. Also suppressed due to thinness.

  32. Vortex drag in thin films within vortex metal theory • Perturbatively: U – screened inter-layer potential. - Density response function (diffusive FL) (Kamenev, Oreg) Drag generically proportional to MR slope. • Expect: (Following von Oppen, Simon, Stern, PRL 2001) • Answer:

  33. Vortex drag in thin films: Results • Our best chance (with no J tunneling) is the highly insulating InO: • maximum drag: Note: similar analysis for SC-metal ‘bilayer’ using a ground plane. Experiment: Mason, Kapitulnik (2001) Theory: Michaeli, Finkel’stein, (2006)

  34. Percolation picture: Coulomb drag • Can neglect drag with the SC islands: • Normal-Normal drag – use results for disorder localized electron glass: (Shimshoni, PRL 1987) • Solve a 2-layer resistor network with drag. - Normal - SC

  35. Percolation picture: Results • Drag resistances: • Solution of the random resistor network: Compare to vortex drag: ?

  36. Conclusions • Vortex picture and the puddle picture: similar single layer predictions. • Giaever transformer bilayer geometry may qualitatively distinguish: • Large drag for vortices, small drag for electrons, with opposite signs. • Drag in the limit of zero interlayer tunneling: vs. • Intelayer Josephson should increase both values, and enhance the effect. (future theoretical work) • Amorphous thin-film bilayers will yield interesting complementary information about the SIT.

  37. Conclusions • What induces the gigantic resistance and the SC-insulating transition? • What is the nature of the insulating state? Exotic vortex physics? Phenomenology: • Vortex picture and the puddle picture: similar single layer predictions. Experimental suggestion: • Giaever transformer bilayer geometry may qualitatively distinguish: • Large drag for vortices, small drag for electrons.

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