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Andreev Reflection ( PCAR ) Spectroscopy Spin Polarization Superconducting Gap Pseudogaps ?  Summary

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Andreev Reflection ( PCAR ) Spectroscopy Spin Polarization Superconducting Gap Pseudogaps ?  Summary Feb. 04, University of Virginia 1 2008 of IRON Superconductors Outline Introduction Point Contact (PC) spectroscopy Spin Transfer Torque ( STT ) Effects Point Contact Andreev Reflection ( PCAR ) spectroscopy Spin polarization Superconducting gap Pseudogaps ? Summary 4 Discovery of Superconductivity Liquefied Helium (1908), b.p. = 4.17 K Discovered superconductivity (1911) in Hg T C = 4.21 K Nobel prize (1913) Heike Kamerlingh Onnes ρ T 0 C T The saga of superconductivity began. 5 Perfect Conductivity and Perfect Diamagnetism Zero resistance Perfect conductivity I Persistent current I over 10 5 years Meissner effect Perfect diamagnetism No field inside SC 6 Type I and Type II Superconductors Type I (Pb, Al, etc) Type II (NbTi, Nb 3Sn, etc) B ≠ 0 B = 0 B = 0 Meissner (H < H C1 ) Meissner (H < H C) Mixed state (H C1 < H < H C2 ) HC2 (0) very large HC(0) ≈ 0.1 Tesla 7 Vortices in Mixed State Abrikosov Vortex Lattices in Superconductors (1957) Nobel Prize (2003) 2 ΦΦΦοοο = hc/2e ≈ 20 G-µm Hess (1989) (STM, NbSe ) Essmann (1967) (Bitter, Pb) 2 8 Josephson Effect 1962 Theoretical prediction of Josephson effect 1973 Nobel prize SC1 SC2 = φ Brian D. Josephson I(t) IC sin( (t)) φ: phase difference h − Φ = = .2 067833636 ×10 15 Wb 0 2e Superconducting Quantum Interference Device (SQUID ) Most sensitive detector 9 Bardeen-Cooper-Schrieffer (BCS) Theory (1957) e ξ e Cooper pairs Bardeen-Cooper-Schrieffer Nobel Prize, 1972 Superconducting Gap ∆∆∆(0)(0)(0) ∆∆∆ 2 /kBTC = 3.53 Eg = 2 10 Very large H c2 for Type II Superconductors High H C2 is necessary Superconducting magnets Magnetic levitation High TC is always beneficial 11 TC vs. Discovery Year 12 Discovery of Cuprates (1986) Discovered (La-Ba)2CuO 4 in 1986, T C = 30 K Nobel prize, 1987 Alex Müller and Georg Bednorz CuO 2 Plane La 2CuO 4 (La-Sr)2CuO 4 (La-Ba)2CuO 4 ∼ TC 30 – 40 K 13 Cuprates YBa Cu O T = 90 K 2 3 7 C Cuprates TC Cu chains (La-Sr)2CuO 4 35 K YBa 2Cu 3O7 90 K Bi 2Sr 2Ca 2Cu 3O10 105 K Cu planes TlBa 2Ca 2Cu 3O9 125 K Cu planes HgBa 2Ca 2Cu 3O8 140 K Cu chains Cu O Cu CuO 2 plane Responsible for high T and a host of unusual properties C 14 TC vs. Discovery Year 15 Mind the Gap 16 s-wave and p-wave Superconductor ∆ s-wave ( isotropic ) Fermi sea Conventional SC (Nb, Pb, Al,…) TC < 25 K + p-wave 3 Fermi sea Superfluid He, Sr 2RuO 4(?) ∼ TC 1 mK - 1 K - 17 d-wave Superconductor Fisher et al., RMP 79 , 353 (2007) + - Fermi sea - + d 2 2 x − y d-wave symmetry Parent compound: Mott insulator Cuprates: CuO 2 plane TC < 160 K 18 New Oxypnictides Fe Superconductors (2008) “Single layer” SmFeAsO Pnictogen (P, As, Sb) (SmO) + (FeAs) - (SmO) + No CuO 2 plane Contains Fe Contains As 19 Discovery of Fe-Superconductors (2008) (SDW) TSDW TC New Fe-SC: ∼ SmFeAsO 1-xFx (1111) TC 55K Parent compound: SmFeAsO metallic Spin density wave ( SDW ) ∼ 160K 20 Fe -Superconductors New Fe-SC: ∼ SmFeAsO 1-xFx (1111), TC 55K Parent compound: SmFeAsO metallic Spin density wave ( SDW ) at 160K ∆ = ? What value ? What structure ? What temperature dependence ? Are there pseudogaps ? 21 Point Contact I+ ρ = V+ RMaxwell a >> l, diffusive I- 2a 4ρl 3π a V- R = 1( + ) Wexler 3πa2 8 l a 4ρl R = Sharvin 3πa2 a << l, ballistic Maxwell ρρρ : resistivity a : contact size l : mean free path Different regime with different physics Sharvin ρ = 1 µΩ-cm 22 Point Contact Spectroscopy Phonon spectra Phonon I+ Spin transfer torque effect V+ Contact size: a ∼ nm I- Current: I = 1 mA 10 2 V- Current density: j = 10 A/cm Point Contact Andreev Reflection a Spin polarization Superconducting gap Thermal transport ballistic, diffusive … 23 Spin Transfer Torque Effect Contact size: a ∼∼∼ nm Current: I = 1 mA Current density: j = 10 10 A/cm 2 T. Y. Chen, Y. Ji and C. L. Chien, Appl. Phys. Lett. 84 , 380 (2004). T. Y. Chen, Y. Ji, C. L. Chien and M. D. Stiles, Phys. Rev. Lett. 93 , 026601 (2004). T. Y. Chen, S. X. Huang, C. L. Chien and M. D. Stiles, Phys. Rev. Lett. 96 , 207203 (2006). 24 Spin Polarization ( P) N (E ) − N (E ) P = ↑ F ↓ F 0 + N(E F): density of states at Fermi energy N↑ (EF ) N↓ (EF ) P: crucial for spintronics 25 Point Contact Andreev Reflection ( PCAR ) I+ Tip: V+ Conducting, semiconducting, I- superconducting V- a Sample: Conducting, semiconducting, superconducting Normal metal/superconductor interface : Andreev Reflection Measures spin polarization (P) and superconducting gap (∆∆∆) 26 Determination of Spin Polarization by PCAR Normal metal /SuperconductorHalf metal /Superconductor Any metal/ Superconductor -∆∆∆ +∆∆∆ -∆∆∆ +∆∆∆ -∆∆∆ +∆∆∆ 0 < P < 1 G(0)/ Gn = 2(1-P) G(0)/ G = 2 P = 0G(0)/ G = 0 P = 1 P of metal,n and ∆∆∆ of SC cann be determined. Ideal contact, clean limit 27 Interfacial Scattering ( Z) and inelastic scattering ( ΓΓΓ) Interfacial: Z suppresses in-gap conductance Inelastic: ΓΓΓ affects conductance at gap Thermal: T smears out conductance Analyzing entire conductance Blonder-Tinkham-Klapwijk (BTK) theory 28 Point Contact Andreev Reflection Spectroscopy Using known SC (Nb, Pb) to determine P of metal • S. X. Huang, T. Y. Chen, and C. L. Chien, Appl. Phys. Lett. 92 , 242509 (2008). • T. Y. Chen, C. L. Chien and C. Petrovic, Appl. Phys. Lett. 91 , 142505 (2007). • C. Leighton, M. Manno, A. Cady, J. W. Freeland, L. Wang, K. Umemoto, R. M. Wentzcovitch, T. Y. Chen, C. L. Chien, P. L. Kuhns, M. J. R. Hoch, A. P. Reyes, W. G. Moulton, E. D. Dahlberg, J. Checkelsky and J. Eckert, J. Phys.: Condens. Matter 19 , 315219(2007) (invited review). • L. Wang, T. Y. Chen, C. L. Chien, and C. Leighton, Appl. Phys. Lett. 88 , 232509 (2006). • L. Wang, T. Y. Chen, C. L. Chien, J. G. Checkelsky, J. C. Eckert, E. D. Dahlberg, K. Umemoto, R. M. Wentzcovitch , and C. Leighton, Phys. Rev. B 73 , 144402 (2006). • L. Wang, K. Umemoto, R.M. Wentzcovitch, T. Y. Chen, C.L. Chien, J.G. Checkelsky, J.C. Eckert, E.D. Dahlberg and C. Leighton, Phys. Rev. Lett. 94 , 056602 (2005). • L. Wang, T. Y. Chen and C. Leighton, Phys. Rev. B 69 , 094412 (2004). • Lance Ritchie and Gang Xiao, Y. Ji, T. Y. Chen, C. L. Chien, Ming Zhang, Jinglan Chen, Zhuhong Liu, Guangheng Wu, and X. X. Zhang, Phys. Rev. B 68 , 104430 (2003). Using known metal (Au, Co) to determine Gap of SC Nb, MgB 2, SmFeAsO 0.85 F0.15 T. Y. Chen, Z. Tesanovic, R. H. Liu, X. H. Chen, and C. L. Chien, Nature 453 , 1224 (2008) 29 AR Spectroscopy Measurements of Gaps One gap of Nb ( TC = 9.27 K) ∆ Nb = 1.42 meV Two gaps of MgB 2 (TC = 36.5 K) ∆ L = 6.75 meV ∆ S = 2.75 meV 30 Superconducting SmFeAsO 1-xFx (x=0.15, 0.18, 0.30) Gold tip I+ V+ I- V- Fe-SCs 31 SmFeAsO 0.85 F0.15 (T C = 42 K) Small T=4.5K ∆ contact Same 2∆∆ for all G(V) Structure: ∼ isotropic Value: 2∆ = 13.34 ± 0.71 meV ∆ 2 /kBTC = 3.68 close to 3.53 (BCS s -wave) Complications: o Extra features to ± 100 mV due to SC o Slanted background nothing to do with SC mismatch of Fermi energy o Emergence of ZBA due to SC Large contact o Small effect in 9 T field at 4.5K 32 Emergence of Zero Bias Anomaly ( ZBA ) • Emerges systematically • ZBA obscures gap • ZBA due to SC • H field has negligible effect ZBA is a signature of d-wave pairing (???). ZBA depends strongly on B field, whereas gap does not (???). (A scheme to obtain gap structure by subtraction) 33 ZBAs in s-wave Superconductors ZBA is a signature of d-wave pairing (???). d-wave may give ZBA. But, ZBA does not imply d-wave since s-wave also gives ZBA. P. Xiong, G. Xiao, R. B. Laibowitz, Phys. Rev. Lett. 71 , 1907 (1993) 34 Neither Gap nor ZBA depends strongly on H ∆∆∆H = 0.5 T Subtraction does not reveal the superconducting gap 35 Zero Bias Anomaly ( ZBA ) ZBA is a signature of d-wave pairing (???). d-wave may give ZBA. But, ZBA does not imply d-wave since s-wave also gives ZBA. ZBA depends strongly on B field, whereas gap does not (???). (A scheme to obtain gap structure by subtraction) Neither ZBA nor gap depends strongly on B field. Subtraction method does not work. 36 A real gap is independent of contacts SmFeAsO 0.70 F0.30 Ω every 0.3 Small R Large R 37 SmFeAsO 0.82 F0.18 (T C = 46.5 K), SmFeAsO 0.70 F0.30 (T C = 53.75 K) SmFeAsO 0.82 F0.18: TC = 46.5 K ∆ = 7.26 meV ∆ 2 /k BTC = 3.62 SmFeAsO 0.70 F0.30: TC = 53.75 K ∆ = 8.16 meV ∆ 2 /k BTC = 3.52 38 Superconducting Gap Theory: s-wave This work: 3 . 86SmFeAsO 0.85 F0.15 3 . 53 ∆ 2∆ )0( 2 = =4 . 06p-wave 3 . 26SmFeAsO 0.82 F0.18 k T kBTc B C SmFeAsO F 4 . 28d-wave 3 . 25 0.70 0.30 SmFeAsO 1-xFx MgB 2 SmFeAsO 1-xFx Rohlf, Modern Physics Fisher et al., Rev. Mod. Phys. 79, 000353 (2007) 39 Temperature-Dependence of Gap every 0.8 K Double-peak (gap): decreasing splitting decreasing intensity vanishes at T C = 42 K Extra features (due to superconductivity) vanishes at T C = 42 K Asymmetrical background (due to normal state) remains at T > T C SmFeAsO 0.85 F0.15 T.
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