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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

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Tunneling of BEC Solitons (Hulet group) 2 Bright matter wave solitons 10 5 7 Li atoms x 13,000m e M > 10 9 m e 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.

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CDW dielectric response: Classical predictions vs. experiment 3 1.Random pinning model: Littlewood PR B 33 6694 (1986). 2.CF: Coppersmith & Fisher PR A 38 6338 (1988). 3.NM: Narayan & Middleton PR B 49, 244 (1994). 4.ZG: Zettl & Grüner PR B 29 755 (1984); WMG: Wu, Mihaly, & Grüner Solid State Commun. 55 663 (1985). Other ac responses flat below threshold. JHM et al. PR B 31 5229 (1985).

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Nucleation of Charge of Flux Soliton Pairs Q 0 = 2Ne c, internal field JHM, Ordóñez, Prodan PRL 84 1555 (2000); JHM et al. J. Phys. A 36 9209 (2003); S. Coleman, Ann. Phys. 101, 239 (1976). Magnetic blockade effect for Josephson vortex pair nucleation: = Coulomb blockade threshold. E T Coulomb Blockade << E T Classical Energy difference: Widom & Srivastava, Phys. Lett. 114A, 337 (1986).

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E T (Coulomb blockade) increases w/ n impurity 5 Coulomb blockade threshold field: E T = Q 0 /2 A = eN c / A Grüner empirical relation emerges naturally! E T = e c n ch ( n ch = N/A, c = condensate fraction) G. Grüner, Rev. Mod. Phys. 60, 1129 (1988). Derived relation for classical depinning field E cl (Grüner): E cl = 4 e c n ch E T (Coulomb blockade) = E cl /4 Expect E T (C.B.) n i 2 for weak pinning.

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

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7 Explains flat dielectric response u E /u p = 1 u E /u p = 0.6 u E /u p = 0.2 u E /u p = 0.015 JHM, Ordóñez, & Prodan PRL 84 1555 (2000). Ross, Wang, & Slichter PRL 56 663 (1986). = u E /u p

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8 h /2 e oscillations in CDW magnetoconductance Latyshev et al, PRL 78, 919 (1997). NbSe 3 with columnar defects h / 2e quantum interference in CDW rings. Tsubota et al, Physica B 404 416–418 (2009). (Tanda group, Hokkaido U., Sapporo, Japan) Contrasts w/ h/2Ne prediction (e.g. Bogachek et al, PRB 42, 7614 (1990) ).

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

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Use of probability amplitudes, TDSE 10 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: Time-dependent Schrödinger equation = “classical” Eq. of motion. [in][in]

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Probability amplitudes, TDSE: Results 11

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

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Probability amplitudes, TDSE: Results (continued) 13 Dotted lines: J cdw ~ [E E Tm ]exp[ E 0 /E] Thorne, Miller, et al, PRL 55, 1006 (1985)

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TDSE: Theory vs. Experiment on dV/dI 14 NbSe 3

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

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h/2e Aharonov-Bohm oscillations in CDW rings 16

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17 Time-varying vector potential Modulates phase of wavefunction TaS 3 – 185 K JHM... Bardeen, PRL 51, 1592 (1983); PRB 31, 5229 (1985); JHM, PhD dissertation (1985). Nonlinear mixing vs. Photon assisted tunneling theory

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“Bells & whistles:” Model with multiple domains 18

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

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

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

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Thickness dependence of I c in YBCO coated conductors 22 Pair creation current, d > : Effective 2D penetration length:

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

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

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Broader implications of model 25 Spontaneous CP violation: “ = ” instability e.g. D. Boer, J. K. Boomsma, PRD 78, 054027 (2008). Michel H. G. Tytgat, PRD 61, 114009 (2000). = 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, Science 312, 1180 (2006).

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Concluding Remarks 26 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.”

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Acknowledgements 27 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, Amitesh Maiti Current collaborators (UH): Asanga I. Wijesinghe, Zhongjia Tang, Arnold M. Guloy Funding: NIH, Texas: Texas Ctr. for Superconductivity

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August 16, 201128 ECRYS 2011 jhmiller@uh.edu Thank you!

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