Vortex drag in a Thin-film Giaever transformer

Transcription

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 (station Q) T. Senthil (MIT)

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

4 Observation of Superconductor-insulator transition Thin amorphous films: tunes a SC-Insulator transition. InO: Saturation as T 0 (Sambandamurthy, (Steiner, Engel, Kapitulnik) Johansson, Shahar, PRL 004) Insulating peak different from sample to sample, scaling different log, activated.

5 Observation of a metallic phase MoGe: (Mason, Kapitulnik, PR 1999)

6 Observation of a metallic phase Ta: (Qin, Vicente, Yoon, 006) Saturation at ~100mK: New metalic phase? (or saturation of electrons temperature)

7 Vortex Paradigm

8 = X-Y model for superconducting film: Cooper pairs as osons When the superconducting order is strong ignore electronic excitations. Standard model for bosonic SF-Ins transition ose-hubbard model : H i j ρ cos( φ ) s j i + Unˆ i [ nˆ, φ] = i ρ S exp[ i ( φ i φ i+ + 1 )] Hopping: Charging energy: Unˆ j Large U - Mott insulator (no charge fluctuations) Large ρ s - Superfluid (intense charge fluctuations, no phase fluctuations) insulator superfluid ρ s /U

9 Vortex description of the SF-insulator transition Vortex hopping: (result of charging effects) tv cos( [ nˆ V, θ ] = i ˆ θ ) Vortex-vortex interactions: 1 r ρ s nv i nv j ln xi x r i, j Condensed vortices = insulating CP s j i j φˆ θˆ Cooper-pairs: Vortices: insulator Vortex: (Fisher, 1990) superfluid ρ s /U V-superfluid V- insulator ρs / t V

10 Universal (?) resistance at SF-insulator transition Assume that vortices and Cooper-pairs are self dual at transition point. Current due to CP hopping: EMF due to vortex hopping: h h π φ & = V V V V = e e τ I = e τ e I Resistance: V πh e h R = = = = 6. 5kΩ I eτ τ 4e 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.

11 Magnetically tuned Superconductor-insulator transition Net vortex density: h e n ˆV = 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. R Disorder pins vortices: Free vortices: Phase coherent SC Vortex SF insulator Disorder localized Electrons: Normal (unpaired)

12 Magnetically tuned Superconductor-insulator transition Net vortex density: h e n ˆV = Problems Saturation of the resistance metallic phase Non-universal insulating peak completely different depending on disorder. R Metallic phase? Disorder localized Electrons: Normal (unpaired)

13 Two-fluid model for the SC-Metal-Insulator transition (Galitski, Refael, Fisher, Senthil, 005) J CP Uncondensed vortices: Cooper-pair channel Finite conductivity: r r j V = σv FV r r E = zˆ j V = σ ˆ r ( z ) V J CP r J CP = 1 σ V r E Disorder inducedgapless QP s (electron channel) (delocalized core states?) r j E r = σ e e Two channels in parallel: r J CP = ( σ + σ e 1 V r ) E

14 Transport properties of the vortex-metal Effective conductivity: σ eff 1 = σ e + σv Assume: - grows from zero to. - grows from zero to infinity. σ e σ N σ V σ e σ V σ N e R eff Vortex metal V Weak insulators: 1 σ e Ta, MoGe Weak InO e < V σ V e V Normal (unpaired)

15 Transport properties of the vortex-metal Effective conductivity: σ eff 1 = σ e + σv Chargless spinons contribute to conductivity! Assume: - grows from zero to. - grows from zero to infinity. σ e σ N σ V σ e σ V σ N e R eff Vortex metal V Strong insulators: TiN, InO e > V σ V V Insulator e 1 σ e Normal (unpaired)

16 More physical properties of the vortex metal Cooper pair tunneling A superconducting STM can tunnel Cooper pairs to the film: G = G e + G CP (Naaman, Tyzer, Dynes, 001).

17 More physical properties of the vortex metal Cooper pair tunneling G CP A superconducting STM can tunnel Cooper pairs to the film: Vortex metal phase: 1 ~ exp( σ ln T ) V T CP G = G e + G CP Normal phase: G e ~ σ e CP Vortex metal R eff e e G G CP strongly T dependent σ V V Insulator e 1 σ e Normal (unpaired) G G ~ 1/ ln e T

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

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

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

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

22 Magneto-resistance curves in the percolation picture Simulate film as a resistor network: (Dubi, Meir, Avishai, 006) NOR island Nor-SC links: SC island R 0 T E G / ~ R e Normal links: SC-SC links: R ~ R e 0 ( ε + ε + ε ε ) / kt 1 1 α R ~ T Reuslting MR:

23 Drag in a bilayer system

24 Giaever transformer Vortex drag Two type-ii bulk superconductors: V R D = I 1 (Giaever, 1965) V i D I 1 Vortices tightly bound: V 1 V1 V = V 1 R D = = R1 I 1

25 Two thin electron gases: DEG bilayers Coulomb drag V R D = I V 1 i D I 1 V 1 Coulomb force creates friction between the layers. Inversely proportional to density squared: Opposite sign to Giaever s vortex drag. R D n 1 e

26 Two thin electron gases: DEG bilayers Coulomb drag V R D = I V 1 i D I 1 Example: ν = 1 T V 1 Excitonic condensate (Kellogg, Eisenstein, Pfeiffer, West, 00)

27 Thin film Giaever transformer V D d Ins ~ 5nm Amorphous (SC) thin films Percolation paradigm d SC ~ 0nm I 1 Insulating layer, Josephson tunneling: J = 0 or J > 0 Vortex condensation paradigm Drag is due to coulomb interaction. Electron density: n ~ d 10 d SC ( QH bilayers: 0 n d cm 3 10 ~ 5 10 Drag suppressed cm cm )? Drag is due to inductive current interactions, and Josephson coupling. Vortex density: n V ~ φ 0 ~ (10 11 [ T ] Significant Drag ) cm

28 Vortex drag in thin films bilayers: interlayer interaction Vortex current suppressed. e.g., Pearl penetration length: λ = eff λ d L SC r Vortex attraction=interlayer induction. Also suppressed due to thinness. U inter qa ( φ0 e q) 1 qa πλ q[( q + λ ) e / λ eff d SC eff eff ] ~ φ0 4πλ ~ eff φ 4λ 0 eff ln( r), r a, r r > λ < a eff

29 Vortex drag in thin films within vortex metal theory R D = V I 1 I 1 V Perturbatively: R D = G drag V ~ [ j 1, j] A 1 U e j1 U e j A (Kamenev, Oreg) Expect: G drag V σσ σ σ V1V 1 V V n Vn 1V 1 nv n V R R 1 Drag generically proportional to MR slope. (Following von Oppen, Simon, Stern, PRL 001) Answer: R D = G drag V = e φ0 4 8π T R1 R dω dq q 3 U Im χ1 Im χ sinh ( ω / T ) U screened inter-layer potential. χ - Density response function (diffusive FL)

30 Vortex drag in thin films: Results R D = G drag V = e φ0 4 8π T R1 R dω dq q 3 U Im χ1 Im χ sinh ( ω / T ) Our best chance (with no J tunneling) is the highly insulating InO: maximum drag: max R D ~ 0. 1mΩ Note: similar analysis for SC-metal bilayer using a ground plane. Experiment: Mason, Kapitulnik (001) Theory: Michaeli, Finkel stein, (006)

31 Percolation picture: Coulomb drag Solve a -layer resistor network with drag. - Normal - SC Can neglect drag with the SC islands: D D R SC, R 0 SC SC NOR Normal-Normal drag use results for disorder localized electron glass: R D NOR NOR = 1 96π R1R h / e ( e n e T a d film ) 1 ln x 0 (Shimshoni, PRL 1987)

32 Drag resistances: Percolation picture: Results D D R SC, R 0 SC SC NOR R D NOR NOR = 1 96π R1R h / e ( e n e T a d film ) ln 1 x 0 Solution of the random resistor network: Compare to vortex drag:?

33 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: R vortex D 1 percolation R D 11 ~ 0. mω vs. ~ 10 Ω 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.

34 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.