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Title 0:40

Vortex matter dynamics and thermodynamics and nanoSQUID on a tip. Title 0:40. Vortex energies 1:40. Bi 2 Sr 2 Ca Cu 2 O 8+ d. CuO 2. Elastic energy. J & EM coupling. CuO 2. Pinning potential. Thermal energy. Driving potential. CuO 2. Lattice constant. Interlayer separation. H.

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Title 0:40

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  1. Vortex matter dynamics and thermodynamics and nanoSQUID on a tip Title 0:40

  2. Vortex energies 1:40 Bi2Sr2CaCu2O8+d CuO2 Elastic energy J & EM coupling CuO2 Pinning potential Thermal energy Driving potential CuO2 Lattice constant Interlayer separation H Disorder-induced fluctuations Normal Thermal fluctuations Skin depth Mixed Meissner T H Intro / Vortex Matter Bi2Sr2CaCu2O8+d Finite Temperature Quenched Disorder Energy scales: Elasticity Drive Length scales:

  3. Outline 1:00 Outline Introduction The vortex system Vortex thermodynamics Equilibrium at low temperatures with vortex shaking First-order melting transition Second-order glass transition Vortex dynamics R(T) – Transport vs. self-induced-field Critical dynamics at the glass transition NanoSQUID on tip

  4. Local magnetiz. 2:00 Micro-Hall sensor array B = V / RHI V 150mm ? Liquid 10x10 mm2 H EPin Bragg Glass I EEl ET -10 32 K Non Equilibrium B – H (G) DB EPin+EEl -20 350 410 H (Oe) Local magnetization in BSCCO Method / Equilibrium 80 K 1st order 0 -5 0 100 H (Oe)

  5. Shaking 1:20 z H z ? y Liquid J H X Z x Bragg Glass Non Equilibrium HDC x HAC Method / ‘Shaking’ A.E. Koshelev, Phys. Rev. Lett.83, 187 (1999) G.P. Mikitik and E.H. Brandt, Phys. Rev. B69, 134521 (2004) Equilibrium 1st order

  6. FOT 1:20 z ? ? Liquid DB Bragg Glass dB / dH -10 32 K Non Equilibrium B – H (G) HDC DB -20 x HAC 350 410 H (Oe) First-order melting Glass Equilibrium 1st order 80 K 0 shake no shake -5 N. Avraham et al., Nature411, 451 (2001) H. Beidenkopf et al., Phys. Rev. Lett.95, 257004 (2005) 0 100 H (Oe)

  7. SOT 1:50 T (K) 600 420 Oe Glass Liquid 500 400 EPin ET 300 ET Bragg Glass 200 350 Oe EPin+EEl EPin+EEl 100 30 35 40 45 50 Second-order glass transition 380 Oe B (G) B –aT (G) Bragg Glass Glass liquid Lattice ?!!? T (K) H. Beidenkopf et al., Phys. Rev. Lett.95, 257004 (2005)

  8. Phase diagram 1:50 1st order 2nd order Phase diagram / Lindemann EPin ~ ET Amorphous Glass Liquid (Gas) EPin ~ EEl ET~ EEl ? Bragg Glass Abrikosov Lattice EPin < ET< EEl

  9. Theory 0:40 1000 900 RSB Liquid RS Liquid Liquid Pinned Liquid 800 Liquid 1st order 2nd order 700 600 H (Oe) H 1st order melting 500 400 2nd order RSB Bragg Glass Tc , Hc2 ,Gi,a(r)a(r’)~a02Rd(r-r’) 300 RSB Solid Solid RS Solid 200 100 0 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 t=T/Tc T Phase diagram / Theory vs. Experiment 2D LLL GL D. Li, B. Rosenstein, Phys. Rev. Lett.90, 167004 (2003) Elastic model T. Giamarchi, P.L. Doussal, Phys. Rev. Lett. 72, 1530 (1994) T. Nattermann, Phys. Rev. Lett.64, 2454 (1990)

  10. Outline 0:30 Outline Introduction The vortex system Vortex thermodynamics Equilibrium at low temperatures First-order melting transition Second-order glass transition Vortex dynamics R(T) – Transport vs Self-induced-field Critical dynamics at the glass transition NanoSQUID on a tip

  11. Theory dynamics 0:50 Thermally activated, Ohmic:r~e-U/T Liquid Pinned Liquid Critical scaling:r~(T-Tg)a, a~6 H Bragg Glass T Glassy (nonOhmic):r~e-U(j)/T, U(j)~j-0.5 T Glass Liquid H 1st order Non Glassy (Ohmic):r~e-U/T 2nd order Solid Bragg Glass Lattice T Dynamics / Theory & Experiment D.S. Fisher, M.P.A. Fisher, D.A. Huse, Phys. Rev. B43, 130 (1991) R.H. Koch et al., Phys. Rev. Lett.63, 1511 (1989) H. Safar et al., Phys. Rev. Lett.68, 2672 (1992) T. Giamarchi, P. Le Doussal, Phys. Rev. B55, 6577 (1997) D.T. Fuchs et al.,Phys. Rev. Lett. 81, 3944 (1998) or M. Luo, X. Hu, V. Vinokur, arXiv:0902:0858v1

  12. Transport 1:20 B (abu) 100 V 10-1 10-2 Glass transition 10-3 10-4 10-5 10-6 Pb, 0.5 T 10-7 Transport noise 10-8 10-9 10-10 30 40 50 60 70 80 90 100 Transport Transport noise level Poor c-axis current penetration R. Busch et al.,Phys. Rev. Lett.69, 522 (1992) B. Khaykovich et al.,Phys. Rev. B 61, R9261 (2000) 350 Oe R (W) c-axis T (K)

  13. Self induced B 2:00 100 V 10-1 j(1) j(1) 10-2 edge bulk 10-3 B(1) B(1) 10-4 10-5 x x 10-6 Pb, 0.5 T 10-7 Transport noise 10-8 10-9 10-10 30 40 50 60 70 80 90 100 Self Induced Field Transport noise level Poor c-axis current penetration Edges shunt bulk edge bulk 350 Oe Glass transition R (W) c-axis T (K) D.T. Fuchs et al., Nature391, 373 (1998)

  14. ) ( Edge Re 3:00 217 Hz 7 Hz 1 Hz 10-1-103 Hz 37 Hz f= 791 Hz B(2) (a.u.) 100 V 10-1 Thermally Activated Re(T) 10-2 10-3 10-4 Le=Re 10-5 10-6 Pb, 0.5 T 10-7 Transport noise 10-8 10-9 10-10 30 40 50 60 70 80 90 100 Edge Resistance Transport noise level Poor c-axis current penetration Edges shunt bulk Inductive edges 350 Oe Glass transition Le=490 pH R (W) c-axis E.H. Brandt et al., PRB 74, 094506 (2006) T (K) H. Beidenkopf et al., PRB 80, 224526 (2009)

  15. ) ( Bulk Rb 2:30 10-1-103 Hz 1 Hz 7 Hz 37 Hz 217 Hz edge j(1) B(1) (a.u.) 0 bulk screened f= 791 Hz 27K B(1) 100 V 10-1 x 10-2 Thermally Activated Rb(T) 10-3 10-4 Lb=Rb 10-5 10-6 Pb, 0.5 T 10-7 Transport noise 10-8 10-9 10-10 30 40 50 60 70 80 90 100 Bulk Resistance at Tg Transport noise level Poor c-axis current penetration Edges shunt bulk Inductive edges and bulk Critical: R~(T-Tg)a 350 Oe Glass transition Le=490 pH Lb=140 pH R (W) Thermally Activated Re(T) c-axis E.H. Brandt et al., PRB 74, 094506 (2006) T (K) H. Beidenkopf et al., PRB 80, 224526 (2009)

  16. ) ( Bulk non ohmic 1:10 Ohmic Non-Ohmic! 30 40 50 Critical: R~(T-Tg)a 100 V 10-1 10-2 Thermally Activated Rb(T) 10-3 10-4 10-5 10-6 Pb, 0.5 T 10-7 Transport noise 10-8 10-9 10-10 30 40 50 60 70 80 90 100 Bulk Resistance at Tg T (K) 350 Oe 300 Oe Glass Liquid H (Oe) 350 300 BrG Glass transition Tg Lattice R, 2pf Lb (W) Thermally Activated Re(T) T (K)

  17. Summary (24:40) 1:10 Liquid Glass BrG Lattice edge bulk Vortex Matter Summary The 1st-order melting and 2nd-order glass transition divide the vortex phase diagram into four thermodynamic phases. New method for measurement of bulk and edge resistance. The inductance of the edge and the bulk dominate the flow at low temperatures. On approaching the glass transition the bulk resistance plunges critically below the thermally activated behavior. The bulk resistance is Ohmic in the liquid phase but non-Ohmic in the lattice phase. H. Beidenkopf et al., PRL 95, 257004 (2005); PRL 98, 167004 (2007); PRB 80, 224526 (2009)

  18. SOT title 1:00 SQUID on a tip Imaging currents and moments on nanoscale A. Finkler, Y. Segev, Y. Myasoedov, M.L. Rappaport and E. Zeldov Weizmann Institute of Science Rehovot, Israel University of Colorado Denver, CO M.E. Huber Harvard University Cambridge, MA J. Martin and A. Yacoby

  19. SQUID operation 1:50 Superconducting Quantum Interference Device (SQUID) I SQUID Josephson junctions Φ=BA Superconducting loop Flux quantization: GL order parameter: Josephson critical current: Superconducting current: SQUID critical current:

  20. SQUID op cont Superconducting Quantum Interference Device (SQUID) 2 I SQUID I / I0 1 Josephson junctions Φ=BA Superconducting loop 0 -4 -2 0 2 4 F / F 0 Flux quantization: GL order parameter: Josephson critical current: Superconducting current: SQUID critical current:

  21. SQUID op cont Superconducting Quantum Interference Device (SQUID) I SQUID Josephson junctions Φ=BA Superconducting loop GL order parameter: Superconducting current: Koshnick et al., Appl. Phys. Lett. 93, 243101 (2008)

  22. SOT fabrication 1:20 100400nm 1 mm SQUID-on-a-tip fabrication

  23. SOT fabrication cont SQUID-on-a-tip fabrication 100400nm Aluminum

  24. SOT fabrication cont SQUID-on-a-tip fabrication Aluminum

  25. SOT fabrication cont SQUID-on-a-tip fabrication Aluminum

  26. SOT fabrication cont Al lead Al lead SQUID loop weak links SQUID-on-a-tip fabrication Aluminum

  27. SOT SEM 1:30 Al lead quartz Al lead Al lead bare quartz Al lead SQUID loop 200 nm SQUID on a tip Pulled quartz tube 200 µm A. Finkler et al., Nano Letters (2010)

  28. SOT interference 2:20 Al lead quartz Al lead SQUID loop 200 nm Flux sensitivity = 2×10-60/Hz1/2 Period = 60.8 mT Loop diameter = 208 nm I0 = 1.6 A  = 2LI0/0 = 0.85 Field sensitivity = 10-7 T/Hz1/2 Spin sensitivity = 65 B/Hz1/2 Lk = 550 pH (Lg = 0.3 pH) SQUID on a tip Quantum interference patterns SQUID current 120 100 V [ mV ] 80 60 -0.1 -0.05 0 0.05 0.1 B [ T ] A. Finkler et al., Nano Letters (2010)

  29. SOT high fields 0:50 Al lead quartz Al lead SQUID loop 200 nm SQUID on a tip Quantum interference patterns SQUID current 100 50 V [ mV ] 0 -50 -100 Flux sensitivity = 2×10-60/Hz1/2 -0.4 -0.2 0 0.2 0.4 B [ T ] Field sensitivity = 10-7 T/Hz1/2 Spin sensitivity = 65 B/Hz1/2 Operational field > 0.5 T A. Finkler et al., Nano Letters (2010)

  30. SOT smallest 0:30 Al lead quartz Al lead SQUID loop 200 nm SQUID on a tip Quantum interference patterns SQUID current Period = 190 mT Loop diameter = 115 nm

  31. SOT VL B calcul 1:20 Al lead quartz Al lead SQUID loop 200 nm SQUID on a tip Calculated vortex lattice field B(x,y) Z=15 nm above surface NbSe2,=132 nm, B = 750 G [G] Y [nm] X [nm] Field modulation decays as exp(-2Z/a0) Factor of 10 every 65 nm in height Flux sensitivity = 2×10-60/Hz1/2 Field sensitivity = 10-7 T/Hz1/2 Spin sensitivity = 65 B/Hz1/2

  32. SSAA SQUID on tip I-V characteristics SOT I-V 0:50 5 k Rs SQUID ontip Rb Vin ISOT T = 300 mK

  33. SOT Noise spectra 0:50 SQUID on tip noise Sn = 1.810-60/Hz1/2

  34. SEM tuning fork 0:40 SQUID on tip glued to tuning fork Quartz tuning fork SQUID on tip 100 µm

  35. SOT meander 1:40 Topographic and magnetic imaging with SQUID on tip Magnetic field at various heights Measured Calculated SQUID on tip ×100 Applied current in meander 2 mA Measurement of topography

  36. Scanning nano-SQUID microscope SPM moving VL 0:50 Magnetic field of a vortex lattice

  37. Scanning nano-SQUID microscope SPM QD CNT 1:20 Spin sensitivity 65 B/Hz1/2 Quantum dot on a carbon nanotube Orbital moment of a single electron 25 B F. Kuemmeth, S. Ilani, D. C. Ralph, and P.L. McEuen, Nature452, 448 (2008).

  38. SPM CNT Wigner Scanning nano-SQUID microscope V.V. Deshpande and M. Bockrath, Nature Physics 4, 314 (2008). Wigner crystal in CNT

  39. Spin sensitivity 2:00 Field sensitivity / Hz1/2 Scanning -SQUIDs SQUID on tip Sensor-sample separation Diamond NV sensor Magnetic moment sensitivity / Hz1/2 Magnetic field and spin sensitivity C. Degen, Nature Nanotech. 3, 643 (2008)

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