Download - Quantum Nucleation of Charge & Flux Solitons
![Page 1: Quantum Nucleation of Charge & Flux Solitons](https://reader036.vdocuments.site/reader036/viewer/2022062222/56816756550346895ddc0d17/html5/thumbnails/1.jpg)
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 - 2011August 16, 2011
![Page 2: Quantum Nucleation of Charge & Flux Solitons](https://reader036.vdocuments.site/reader036/viewer/2022062222/56816756550346895ddc0d17/html5/thumbnails/2.jpg)
Tunneling of BEC Solitons (Hulet group)
2
Bright matter wave solitons
105 7Li atoms x 13,000me
M > 109 me
Macroscopic wavefunctions tunnel through opticalbarrier (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.
![Page 3: Quantum Nucleation of Charge & Flux Solitons](https://reader036.vdocuments.site/reader036/viewer/2022062222/56816756550346895ddc0d17/html5/thumbnails/3.jpg)
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).
![Page 4: Quantum Nucleation of Charge & Flux Solitons](https://reader036.vdocuments.site/reader036/viewer/2022062222/56816756550346895ddc0d17/html5/thumbnails/4.jpg)
Nucleation of Charge of Flux Soliton Pairs
Q0 = 2Nerc, 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.
ET Coulomb Blockade << ET Classical
Energy difference:
Widom & Srivastava, Phys. Lett. 114A, 337 (1986).
![Page 5: Quantum Nucleation of Charge & Flux Solitons](https://reader036.vdocuments.site/reader036/viewer/2022062222/56816756550346895ddc0d17/html5/thumbnails/5.jpg)
ET (Coulomb blockade) increases w/ nimpurity
5
Coulomb blockade threshold field: ET = Q0/2e A = eNrc /e A Grüner empirical relation emerges naturally!
e ET = ercnch (nch = N/A, rc = condensate fraction)
G. Grüner, Rev. Mod. Phys. 60, 1129 (1988).
Derived relation for classical depinning field Ecl (Grüner):
e Ecl = 4percnch
ET (Coulomb blockade) = Ecl /4p
Expect ET (C.B.) ni
2 for weak pinning.
![Page 6: Quantum Nucleation of Charge & Flux Solitons](https://reader036.vdocuments.site/reader036/viewer/2022062222/56816756550346895ddc0d17/html5/thumbnails/6.jpg)
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 q > p (or q – 2pn > p).
![Page 7: Quantum Nucleation of Charge & Flux Solitons](https://reader036.vdocuments.site/reader036/viewer/2022062222/56816756550346895ddc0d17/html5/thumbnails/7.jpg)
7
Explains flat dielectric response
uE/up = 1
uE/up = 0.6
uE/up = 0.2
uE/up = 0.015
JHM, Ordóñez, & Prodan PRL 84 1555 (2000).
Ross, Wang, & Slichter PRL 56 663 (1986).
t = uE/up
![Page 8: Quantum Nucleation of Charge & Flux Solitons](https://reader036.vdocuments.site/reader036/viewer/2022062222/56816756550346895ddc0d17/html5/thumbnails/8.jpg)
8
h/2e oscillations in CDW magnetoconductance
Latyshev et al, PRL 78, 919 (1997).
NbSe3 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)).
![Page 9: Quantum Nucleation of Charge & Flux Solitons](https://reader036.vdocuments.site/reader036/viewer/2022062222/56816756550346895ddc0d17/html5/thumbnails/9.jpg)
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:
![Page 10: Quantum Nucleation of Charge & Flux Solitons](https://reader036.vdocuments.site/reader036/viewer/2022062222/56816756550346895ddc0d17/html5/thumbnails/10.jpg)
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.
[idn]
![Page 11: Quantum Nucleation of Charge & Flux Solitons](https://reader036.vdocuments.site/reader036/viewer/2022062222/56816756550346895ddc0d17/html5/thumbnails/11.jpg)
Probability amplitudes, TDSE: Results
11
![Page 12: Quantum Nucleation of Charge & Flux Solitons](https://reader036.vdocuments.site/reader036/viewer/2022062222/56816756550346895ddc0d17/html5/thumbnails/12.jpg)
Probability amplitudes, TDSE: Results (continued)
12Solid lines – theory; Dashed Lines - experiment
Experimental data –McCarten group, PRB2000.
9.90 mA
10.89 mA
11.49 mA
11.88 mA
![Page 13: Quantum Nucleation of Charge & Flux Solitons](https://reader036.vdocuments.site/reader036/viewer/2022062222/56816756550346895ddc0d17/html5/thumbnails/13.jpg)
Probability amplitudes, TDSE: Results (continued)
13
Dotted lines:
Jcdw ~ [E ETm]exp[E0/E]
Thorne, Miller, et al, PRL 55, 1006 (1985)
![Page 14: Quantum Nucleation of Charge & Flux Solitons](https://reader036.vdocuments.site/reader036/viewer/2022062222/56816756550346895ddc0d17/html5/thumbnails/14.jpg)
TDSE: Theory vs. Experiment on dV/dI
14
NbSe3
![Page 15: Quantum Nucleation of Charge & Flux Solitons](https://reader036.vdocuments.site/reader036/viewer/2022062222/56816756550346895ddc0d17/html5/thumbnails/15.jpg)
Phase Diagram – Soliton Nucleation vs. Classical Depinning
15
Blue bronze data (Mihaly et al)
![Page 16: Quantum Nucleation of Charge & Flux Solitons](https://reader036.vdocuments.site/reader036/viewer/2022062222/56816756550346895ddc0d17/html5/thumbnails/16.jpg)
h/2e Aharonov-Bohm oscillations in CDW rings
16
![Page 17: Quantum Nucleation of Charge & Flux Solitons](https://reader036.vdocuments.site/reader036/viewer/2022062222/56816756550346895ddc0d17/html5/thumbnails/17.jpg)
17
Time-varying vector potential Modulates phase of wavefunction
TaS3 – 185 K
JHM ... Bardeen, PRL 51, 1592 (1983); PRB 31, 5229 (1985); JHM, PhD dissertation (1985).
Nonlinear mixing vs. Photon assisted tunneling theory
![Page 18: Quantum Nucleation of Charge & Flux Solitons](https://reader036.vdocuments.site/reader036/viewer/2022062222/56816756550346895ddc0d17/html5/thumbnails/18.jpg)
“Bells & whistles:” Model with multiple domains
18
![Page 19: Quantum Nucleation of Charge & Flux Solitons](https://reader036.vdocuments.site/reader036/viewer/2022062222/56816756550346895ddc0d17/html5/thumbnails/19.jpg)
Inclusion of nonlinear terms:
19
g’ = .001 g’ = .01 g’ = .02
![Page 20: Quantum Nucleation of Charge & Flux Solitons](https://reader036.vdocuments.site/reader036/viewer/2022062222/56816756550346895ddc0d17/html5/thumbnails/20.jpg)
20
Alternative approach: Use of Probabilities
Let p = probability f tunnels from branch n to n+1.
Then:
-
![Page 21: Quantum Nucleation of Charge & Flux Solitons](https://reader036.vdocuments.site/reader036/viewer/2022062222/56816756550346895ddc0d17/html5/thumbnails/21.jpg)
Fixed time interval (non-integer # of cycles) used when averaging voltage
21
Theory Experiment (Cornell group)
![Page 22: Quantum Nucleation of Charge & Flux Solitons](https://reader036.vdocuments.site/reader036/viewer/2022062222/56816756550346895ddc0d17/html5/thumbnails/22.jpg)
Thickness dependence of Ic in YBCO coated conductors
22
Pair creation current, d > l: Effective 2D penetration length:
![Page 23: Quantum Nucleation of Charge & Flux Solitons](https://reader036.vdocuments.site/reader036/viewer/2022062222/56816756550346895ddc0d17/html5/thumbnails/23.jpg)
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
![Page 24: Quantum Nucleation of Charge & Flux Solitons](https://reader036.vdocuments.site/reader036/viewer/2022062222/56816756550346895ddc0d17/html5/thumbnails/24.jpg)
Superconducting iron pnictide bi-crystal junction
24
Data from X. Zhang et al., APL 95, 062510 (2009).
4.2 K
![Page 25: Quantum Nucleation of Charge & Flux Solitons](https://reader036.vdocuments.site/reader036/viewer/2022062222/56816756550346895ddc0d17/html5/thumbnails/25.jpg)
Broader implications of model
25
Spontaneous CP violation: “q = p” instability e.g. D. Boer, J. K. Boomsma, PRD 78, 054027 (2008). Michel H. G. Tytgat, PRD 61, 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 universeTunneling of universe small ( 0) cosmological constant
e.g. P. J. Steinhardt, N. Turok, Science 312, 1180 (2006).
![Page 26: Quantum Nucleation of Charge & Flux Solitons](https://reader036.vdocuments.site/reader036/viewer/2022062222/56816756550346895ddc0d17/html5/thumbnails/26.jpg)
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.”
![Page 27: Quantum Nucleation of Charge & Flux Solitons](https://reader036.vdocuments.site/reader036/viewer/2022062222/56816756550346895ddc0d17/html5/thumbnails/27.jpg)
Acknowledgements
27
Previous collaborators: John Tucker, John Bardeen, UIUCDocumentary, 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