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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.

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Presentation on theme: "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."— Presentation transcript:

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 ECRYS August 16, 2011

2 Tunneling of BEC Solitons (Hulet group) 2 Bright matter wave solitons 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.

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

4 Nucleation of Charge of Flux Soliton Pairs  Q 0 =  2Ne  c,  internal field JHM, Ordóñez, Prodan PRL (2000); JHM et al. J. Phys. A (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).

5 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.

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

7 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 = JHM, Ordóñez, & Prodan PRL (2000). Ross, Wang, & Slichter PRL (1986).  = u E /u p

8 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 –418 (2009). (Tanda group, Hokkaido U., Sapporo, Japan) Contrasts w/ h/2Ne prediction (e.g. Bogachek et al, PRB 42, 7614 (1990) ).

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

10 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. [in][in]

11 Probability amplitudes, TDSE: Results 11

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

13 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)

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

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

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

17 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

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

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

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

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

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

23 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

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

25 Broader implications of model 25 Spontaneous CP violation: “  =  ” instability e.g. D. Boer, J. K. Boomsma, PRD 78, (2008). Michel H. G. Tytgat, PRD 61, (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).

26 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.”

27 Acknowledgements 27 Previous collaborators: John Tucker, John Bardeen, UIUC Documentary, book: the-University-of-Illinois.html Articles about and by John Bardeen: David Pines, Physics Today, April Proc. Am. Phil. Soc. 153, 287 (2009). John Bardeen, Physics Today, December 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

28 August 16, ECRYS 2011 Thank you!


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