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SIT and MQT in 1D

SIT and MQT in 1D (Superconductor-insulator transition and macroscopic quantum tunneling in quasi-one-dimensional superconducting wires) Alexey Bezryadin Department of Physics University of Illinois at Urbana-Champaign. Acknowledgments. Experiment:

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SIT and MQT in 1D

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  1. SIT and MQT in 1D (Superconductor-insulator transition and macroscopic quantum tunneling in quasi-one-dimensional superconducting wires) Alexey Bezryadin Department of Physics University of Illinois at Urbana-Champaign

  2. Acknowledgments Experiment: Andrey Rogachev – former postdoc; now at Utah Univ. Myung-Ho Bae – postdoc. Tony Bollinger – PhD 2005; now staff researcher at BNL Dave Hopkins – PhD 2006; now at LAM research Robert Dinsmore –PhD 2009; now at Intel Mitrabhanu Sahu –PhD 2009; now at Intel Matt Brenner –grad student Theory: David Pekker Tzu Chieh Wei Nayana Shah Paul Goldbart

  3. Outline • Motivation • Fabrication of superconducting nanowires and our measurement setup • Source of dissipation: Little’s phase slip • Evidence for SIT • Evidence for MQT of phase slips (i.e. observation of QPS) - Conclusions

  4. Motivation (SIT) 2D Approaching 1D R_sq_c~6.5kOhm R_sq_c~6.5kOhm • D. B. Haviland, Y. Liu, and A. M. Goldman, Phys. Rev. Lett.62, 2180 (1989). • P. Xiong, A.V. Herzog, and R.C. Dynes, Phys. Rev. Lett.78, 927 (1997).

  5. Motivation (MQT) - Leggett initiates the field of macroscopic quantum physics. Macroscopic quantum phenomena can occur and can be theoretically described (Leggett ‘78). (A superposition of macroscopically distinct states is the required signature of truly macroscopic quantum behavior) [1,2,3]. - Macroscopic quantum tunneling (MQT) was clearly observed and understood in Josephson junctions (Clarke group ‘87) but not on nanowires. [4]. - MQT is proposed as a mechanism for a new qubit design (Mooij-Harmans ‘05) [5]. - Quantum phase slip in superconducting wires may have interesting device applications, e.g. in fundamental current standards (Mooij-Nazarov‘06) [6]. • Leggett, A. J. J. Phys. Colloq.(Paris), 39, C6-1264 (1978). • Caldeira, A.O. & Legget, A.J. Phys. Rev. Lett.46, 211 (1981). • Great book on MQT: S. Takagi. Macroscopic quantum tunneling. • Cambridge University Press, 2002. • 4. Martinis, J. M., Devoret, M. H. & Clarke, J. Phys. Rev. B 35, 4682 (1987). • 5. Mooij, J. E. & Harmans, C. J. P. M. New J. Phys.7, 219 (2005). • 6. Mooij, J. E. & Nazarov Y. V. Nature Physics 2, 169 (2006).

  6. Sample Fabrication Method of Molecular Templating Si/ SiO2/SiN substrate with undercut ~ 0.5 mm Si wafer 500 nm SiO2 60 nm SiN Width of the trenches ~ 50 - 500 nm HF dip for ~10 seconds R_square=200 μΩ cm/10 nm=200 Ω A. Bezryadin, C.N. Lau, and M. Tinkham, Nature404, 971 (2000)

  7. 4 nm Sample Fabrication Schematic picture of the pattern Nanowire + Film Electrodes used in transport measurements TEM image of a wire; Nominal thickness = 3 nm (Mikas Rimeika) R_square=200 μΩ cm/10 nm=200 Ω

  8. Measurement Scheme Sample mounted on the 3He insert. Circuit Diagram

  9. Tony Bollinger's sample-mounting procedure in winter in Urbana • Procedure (~75% Success) • - Put on gloves • - Put grounded socket for mounting in vise with grounded indium dot tool connected • - Spray high-backed black chair all over and about 1 m square meter of ground with anti-static spray • - DO NOT use green chair • - Not sure about short-backed black chairs • - Sit down • - Spray bottom of feet with anti-static spray • - Plant feet on the ground. Do not move your feet again for any reason until mounting is finished. • - Mount sample • - Keep sample in grounded socket until last possible moment • - Test samples in dipstick at ~1 nA

  10. Dichotomy in nanowires  evidence for SIT Parameter: Nominal thickness of the deposited MoGe film A. Bollinger, R. Dinsmore, A. Rogachev and A. Bezryadin, Phys. Rev. Lett. 101, 227003 (2008)

  11. Little’s phase slip ∆(x)=│∆(x)│exp[iφ] William A. Little, “Decay of persistent currents in small superconductors”, Phys. Rev., 156, 396 (1967).

  12. Langer, Ambegaokar, McCumber, Halperin theory (LAMH) The barrier, derived using GL theory  The attempt frequency, using the TDGL theory (due to McCumber and Halperin)  RAL ≈RNexp[-ΔF(T)/kBT] Simplified formula: Arrhenius-Little fit:

  13. origin of quantum phase slips He3 He4 Possible Origin of Quantum Phase Slips

  14. Tunneling junction oxide e e metal metal p.1245 p.4887 Diffusive coherent wire acts as coherent scatterer Barrier shape Barrier shape

  15. R0=17.4 kW Insulating behavior is due to Coulomb blockade Golubev-Zaikin formula

  16. Dichotomy in nanowires: High-bias measurements. Fits: Golubev-Zaikin theory PRL 86, 4887 (2001).

  17. Superconductor-insulator transition phase diagram Possible origin of the SIT: Anderson-Heisenberg uncertainty principle: RN<6.45kΩ RN>6.45kΩ A. Bollinger, R. Dinsmore, A. Rogachev and A. Bezryadin, Phys. Rev. Lett.101, 227003 (2008)

  18. RN I φ1 φ2 C RCSJ Model of a Josephson junction Stewart-McCumber RCSJ model (ћ C/2e) d2φ/dt2 + (ћ/2eRN ) dφ/dt+ (2e EJ/ ћ) sinφ = I (from Kirchhoff law) Particle in a periodic potential with damping : classical Newton equation md2x/dt2 + ηdx/dt– dU(x)/dx = Fext

  19. Schmid-Bulgadaev diagram A. Schmid, Phys. Rev. Lett., 51, 1506 (1983) S. A. Bulgadaev, “Phase diagram of a dissipative quantum system.” JETP Lett. 39, 315 (1984). EJ /EC Insulator Superconductor RQ/RN 1 RQ= h/4e2=6.45kΩ

  20. Theoretical approach to our data LAMH applies if:

  21. Switching current in thin wires: search for QPS V-I curves High Bias-Current Measurements

  22. Switching and re-trapping currents vs. temperatures MoGe Nanowire

  23. Switching Current Distributions ΔT=0.1 K # 10,000 Bin size = 3 nA ! The widths of distributions increases with decreasing temperature ! M. Sahu, M. Bae, A. Rogachev, D. Pekker, T. Wei, N. Shah, P. M. Goldbart, A. Bezryadin Accepted in Nature Physics (2009).

  24. Voss and Webb observe QPS (MQT) in 1981 “Macroscopic Quantum Tunneling in 1 micron Nb junctions” By Richard Voss and Richard Webb, Phys. Rev. Lett.47, 265 (1981) Switching current distributions of a single 1-μm Nb junction.

  25. Voss and Webb: width of the switching current distribution vs. T R. Voss and R. Webb PRL 47, 265 (1981)

  26. Temperature dependence of the widths of the distributions Widths decrease with increasing temperature. Sahu, M. et al. (arXiv:0804.2251v2)

  27. Switching rate out of the superconducting state FD Derived switching rates Experimental data Here, K=1 the channel in the distribution with the largest value of the current . ΔI, is the bin width in the distribution histograms. T.A. Fulton and L.N. Dunkleberger, Phys. Rev. B9, 4760 (1974).

  28. MQT in high-TC Josephson junctions T* M.-H. Bae and A. Bezryadin, to be published

  29. A single phase slip causes switching due to overheating(one-to-one correspondence of phase slips and switching events) Tails due to multiple phase-slips

  30. Model of stochastic switching dynamics Competition between heating caused by each phase slip event cooling At higher temperatures a larger number of phase slips are required to cause at switching. At low enough temperatures a single phase slip is enough to cause switching. Thus there is one-to-one correspondence between switching events and phase slips! 1. M. Tinkham, J.U. Free, C.N. Lau, N. Markovic, Phys. Rev. B68,134515 (2003). 2. Shah, N., Pekker D. & Goldbart P. M.. Phys. Rev. Lett.101, 207001 (2008).

  31. Simulated temperature bumps T = 1.9 K I = 0.35 μA TC =2.7 K 5 10 (ns) Gradual cooling after a a PS Sharp T bump due to a PS CV(T) and KS(T) decreases as the temperature is decreased. ->Easier to heat the wire due to lower CV and increased ISW

  32. Switching rates at different temperatures TAPS only TAPS and QPS Sahu, M. et al. (arXiv:0804.2251v2)

  33. Crossover temperature T* TAPS rate Giordano formula the for QPS rate 1. Giordano,N. Phys. Rev. Lett.61, 2137 (1988). 2. M. Tinkham, J.U. Free, C.N. Lau, N. Markovic, Phys. Rev. B 68,134515 (2003) and the references therein.

  34. Phase slip rates • For Thermally Activated Phase slips (TAPS) (based on LAMH), where, • For Quantum Phase Slips (QPS),

  35. Switching rate at 0.3K compared to TAPS and QPS T=0.3 K QPS rate TAPS rate Sahu, M. et al. (arXiv:0804.2251v2)

  36. TQPS and T* for different nanowires T* increases with increasing critical current Sahu, M. et al. (arXiv:0804.2251v2), To appear in Nature Physics

  37. T* vs. IC(0)

  38. Preliminary results: shunting the wires Fit with Caldeira-Leggett Fit without dissipation Exact fits: Bardeen microscopic theory M. Brenner and A. Bezryadin, to be published

  39. Conclusions - SIT is found in thin MoGe wires - The superconducting regime obeys the Arrhenius thermal activation of phase slips - The insulating regime is due to weak Coulomb blockade - MQT is observed at high bias currents, close to the depairing current - At sufficiently low temperatures, every single QPS causes switching in the wire. (This is due to the fact that phase slips can only occur very near the depairing current at low T. Thus the Tc is strongly suppressed by the bias current. Thus the Joule heat released by one phase slip needs to heat the wire just slightly to push it above the critical temperature).

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