Quantum Nucleation of Charge & Flux Solitons

1. Quantum Nucleation of Charge & Flux Solitons John H. Miller, Jr. A. I. Wijesinghe, Z. Tang, & A. M. Guloy Dept. of Physics, Dept. of Chemistry, & Texas Center for Superconductivity University of Houston jhmiller@uh.edu ECRYS - 2011 August 16, 2011

2. Tunneling of BEC Solitons (Hulet group) • Bright matter wave solitons • 1057Li atoms x 13,000me • M > 109 me • Macroscopic wavefunctions • tunnel through optical • barrier (w/ transmitted & • reflected components). Tunneling probability: Agrees w/ experiment only if m & V taken to be single atom quantities. Hybrid between Josephson tunneling & MQT. BEC soliton = quantum fluid. Quantum fluid: Each particle delocalized over l > interparticle spacing. CDW = quantum fluid: Each e- delocalized over long distances.

3. CDW dielectric response: Classical predictions vs. experiment JHM et al. PR B 31 5229 (1985). Other ac responses flat below threshold. Random pinning model: LittlewoodPR B 33 6694 (1986). CF: Coppersmith & Fisher PR A 38 6338 (1988). NM: Narayan & Middleton PR B 49, 244 (1994). ZG: Zettl & GrünerPR B 29 755 (1984); WMG: Wu, Mihaly, & Grüner Solid State Commun. 55 663 (1985).

4. Nucleation of Charge of Flux Soliton Pairs Q0 = 2Nerc,  internal field Energy difference: =Coulomb blockade threshold. ET Coulomb Blockade << ET Classical Magnetic blockade effect for Josephson vortex pair nucleation: Widom & Srivastava, Phys. Lett. 114A,337 (1986). JHM, Ordóñez, Prodan PRL 84 1555 (2000); JHM et al. J. Phys. A 36 9209 (2003); S. Coleman, Ann. Phys. 101, 239 (1976).

5. ET (Coulomb blockade) increases w/ nimpurity Coulomb blockade threshold field: ET=Q0/2eA=eNrc/eA Grüner empirical relation emerges naturally! eET=ercnch (nch = N/A, rc = condensate fraction) G. Grüner, Rev. Mod. Phys. 60, 1129 (1988). Derived relation for classical depinning field Ecl(Grüner): eEcl= 4percnch  ET(Coulomb blockade) = Ecl/4p  Expect ET (C.B.)  ni2 for weak pinning.

6. Time Correlated Soliton Tunneling • ‘Vacuum angle’: • Pinning & electrostatic energy (per chain): Tunneling (‘false vacuum’ decay) when q > p (orq – 2pn > p). Charging energy: JHM, Ordóñez & Prodan PRL 84 1555 (2000). JHM, Cárdenas, et al. J. Phys. A 36 9209 (2003); S. Coleman, Ann. Phys. 101, 239 (1976).

7. Explains flat dielectric response uE/up = 1 uE/up = 0.6 t = uE/up uE/up = 0.2 uE/up = 0.015 JHM, Ordóñez, & Prodan PRL 84 1555 (2000). Ross, Wang, & SlichterPRL 56 663 (1986).

8. h/2e oscillations in CDW magnetoconductance h/2e quantum interference in CDW rings. NbSe3 with columnar defects Tsubota et al, Physica B404 416–418 (2009). (Tanda group, Hokkaido U., Sapporo, Japan) Latyshev et al, PRL78, 919 (1997). Contrasts w/ h/2Ne prediction (e.g. Bogachek et al, PRB42, 7614 (1990)).

9. Proposed model to simulate DW dynamics Defining: & yields: Analogous to time-correlated single-electron tunneling (Averin & Likharev, J. Low T. Phys. 62 345 (1986))

10. Use of probability amplitudes, TDSE Motivated by Feynman Lectures, vol. III treatment of Josephson junction. Introduce field-dependent tunneling Hamiltonian matrix element: Amplitude for density wave to be on branch n: [idn] Time-dependent Schrödinger equation = “classical” Eq. of motion.

11. Probability amplitudes, TDSE: Results

12. Probability amplitudes, TDSE: Results (continued) 11.88 mA 11.49 mA 10.89 mA 9.90 mA Experimental data – McCarten group, PRB 2000. Solid lines – theory; Dashed Lines - experiment

13. Probability amplitudes, TDSE: Results (continued) Dotted lines: Jcdw ~ [EETm]exp[E0/E] Thorne, Miller, et al, PRL55, 1006 (1985)

14. TDSE: Theory vs. Experiment on dV/dI NbSe3

15. Phase Diagram – Soliton Nucleation vs. Classical Depinning Blue bronze data (Mihaly et al)

16. h/2eAharonov-Bohm oscillations in CDW rings

17. Time-varying vector potential  Modulates phase of wavefunction Nonlinear mixing vs. Photon assisted tunneling theory TaS3 – 185 K JHM ... Bardeen, PRL51, 1592 (1983); PRB31, 5229 (1985); JHM, PhD dissertation (1985).

18. “Bells & whistles:” Model with multiple domains

19. Inclusion of nonlinear terms: g’ = .001 g’ = .01 g’ = .02

20. Alternative approach: Use of Probabilities Let p = probability f tunnels from branch n to n+1. Then: -

21. Fixed time interval (non-integer # of cycles) used when averaging voltage Theory Experiment (Cornell group)

22. Thickness dependence of Ic in YBCO coated conductors Pair creation current, d > l: Effective 2D penetration length: 

23. V - I curve of YBCO grain boundary junction Classical RSJ model: 82.5K 77.2K 86 K 75K 70K Quantum Simulations (solid lines) Data from R. D. Redwing et al., APL 75, 3171 (1999).

24. Superconducting iron pnictide bi-crystal junction 4.2 K Data from X. Zhang et al., APL 95,062510 (2009).

25. Broader implications of model Spontaneous CP violation: “q = p” instability e.g. D. Boer, J. K. Boomsma, PRD78, 054027 (2008). Michel H. G. Tytgat, PRD61, 114009 (2000). q = p instabilities have also been proposed for: - Quantum Hall effect - Topological Insulators Quantum cosmology: Quantum creation of universe(s) Phase transitions in the early universe Tunneling of universe  small ( 0) cosmological constant e.g. P. J. Steinhardt, N. Turok, Science312, 1180 (2006).

26. Concluding Remarks Quantum theory is the most ubiquitous, universally applicable theory known to man. The laws of quantum physics govern every system of particles in the universe, & probably the universe as a whole. One of those laws (Murray Gell-Mann’s totalitarian principle) is: “Everything not forbidden is compulsory.”

27. Acknowledgements Previous collaborators: John Tucker, John Bardeen, UIUC Documentary, book: http://1m1f.com/video/OyV8qSwGUHU/Spark-of-Genius-The-Story-of-John-Bardeen-at-the-University-of-Illinois.html Articles about and by John Bardeen: David Pines, Physics Today, April 1992. Proc. Am. Phil. Soc. 153, 287 (2009). John Bardeen, Physics Today, December 1990. Previous collaborators (continued): Emil Prodan (currently at Yeshiva U.), Carlos Ordonez (UH), John McCarten, AmiteshMaiti Current collaborators (UH): Asanga I. Wijesinghe, Zhongjia Tang, Arnold M. Guloy Funding: NIH, Texas: Texas Ctr. for Superconductivity

28. Thank you! ECRYS 2011 jhmiller@uh.edu