paul michael grant aps senior life fellow ibm research staff member emeritus epri science fellow...
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Paul Michael GrantAPS Senior Life Fellow
IBM Research Staff Member EmeritusEPRI Science Fellow (Retired)
Principal, W2AGZ Technologies
Does the
Hold the Key to Room Temperature Superconductivity?
Session T41: T41.00008, Room F152, Wednesday, 4:42 PM
Superconducting Fluctuations in One-Dimensional Quasi-periodic Metallic
Chains
Aging IBM Pensioner(research supported under the IBM
retirement fund)
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St. Patrick’s Day - 2010
Bridget Ann Mullen-Whalen
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May, 2028 (still have some time!)
50th Anniversary of Physics Today, May 1998http://www.w2agz.com/Publications/Popular%20Science/Bio-Inspired%20Superconductivity,%20Physics%20Today%2051,%2017%20%281998%29.pdf
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1
*CT a e
“Bardeen-Cooper-Schrieffer”
Where
Q = Debye Temperature (~ 275 K)
l = Electron-Phonon Coupling (~ 0.28)
* = Electron-Electron Repulsion (~ 0.1)
a = “Gap Parameter, ~ 1-3”
Tc = Critical Temperature ( 9.5 K “Nb”)
Fk E
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“3-D”Aluminum,TC = 1.15 K
“Irrational”
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“Put-on !”
Fermion-Boson Interactions
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Diethyl-cyanine iodide
Little, 1963
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1D metallic chains are inherently unstable to dimerization and gapping of the Fermi surface, e.g., (CH)x. Ipso facto, no “1D” metals can exist!
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NanoConcept
What novel atomic/molecular arrangement might give rise to higher temperature superconductivity >> 165 K?
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• Model its expected physical properties using Density Functional Theory.
– DFT is a widely used tool in the pharmaceutical, semiconductor, metallurgical and chemical industries.
– Gives very reliable results for ground state properties for a wide variety of materials, including strongly correlated, and the low lying quasiparticle spectrum for many as well.
• This approach opens a new method for the prediction and discovery of novel materials through numerical analysis of “proxy structures.”
NanoBlueprint
LDA+U LDA HUB DC( ) ( ) l lmE n E n E n E n r r
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Fibonacci Chains
1 2
1 2
6
| , 3, 4,5,...,
Where ,
And lim ( ) / ( ) (1 5) / 2 1.618...
Example: ( 13)
n n n
a n b nn
G G G n
G a G ab
N G N G
G abaababaab N
Let , subject to , invariant,
And take and
to be "inter-atomic n-n distances,"
Then , / (1 ) 1 .
Where is a "scaling" parameter.
a c b a b
a b
b a b c
c
“Monte-Carlo Simulation of Fermions on Quasiperiodic Chains,”
P. M. Grant, BAPS March Meeting (1992, Indianapolis)
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tan = 1/ ; = (1 + 5)/2 = 1.618… ; = 31.717…°
A Fibonacci “Dislocation Line”
STO ?SRO !
Al
Al
Al
Al
Al
Al
Al
L = 4.058 Å (fcc edge) s = 2.869 Å (fcc diag)
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64 = 65
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“Not So Famous Danish Kid Brother”
Harald BohrSilver Medal, Danish Football Team, 1908 Olympic Games
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Almost Periodic FunctionsDefinition I: Set of all summable trigonometric series:
( )
where { } are denumerable.
Type (1) Purely Periodic: , n = 0, 1, 2, ...
Type (2) Limit Periodic: , {ra
ni xn
n
n
n
n n n
f x A e
cn
cr r
tionals}
Type (3) General Case: One or more irrational
==========================================
Definition II: Existence of an infinite set of "translation
numbers," { }, such that:
| ( )
n
f x
2 2
( ) | ; < <
where 0.
==========================================
Parseval's Theorem:
1| | lim | ( ) |
2
Mean Value Theorem:
( ) ( )
L
nL
n L
i xn n
f x x
A f x dxL
f x e dx A
Example : ( ) cos cos 2f x x x
“Electronic Structure of Disordered Solids and
Almost Periodic Functions,”
P. M. Grant, BAPS 18, 333 (1973, San Diego)
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Doubly Periodic Al Chain(a = 4.058 Å [fcc edge], b = c = 3×a)
a
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Doubly Periodic Al Chain(a = 2.869 Å [fcc diag], b = c = 6×a)
a
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Quasi-Periodic Al ChainFibo G = 6: s = 2.868 Å, L = 4.058 Å
(a = s+L+s+s = 12.66 Å, b = c ≈ 3×a)
s s sL
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Conclusions
• 1D Quasi-periodicity can defend a linear metallic state against CDW/SDW instabilities (or at least yield an semiconductor with extremely small gaps)
• Decoration of appropriate surface bi-crystal grain boundaries or dislocation lines with appropriate odd-electron elements could provide such an embodiment.
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Homework• Computational physics and chemistry has attained the potential to
assess the physical possibility of other-than-phonon mediated superconductivity via examination of “proxy structures” such as the example proposed in this talk.
• However, better and more comprehensive “post-processing” software tools are required to supplant and substitute for Eliashberg-McMillan based algorithms.
• The formalism already exists within the framework of the momentum-dependent dielectric function, ε(q, ω+iγ), e.g., the generalized Lindhard expression and/or the work of Kirzhnitz, Maksimov and Khomski……., but no code implementation is currently available (as far as I know…possibly soon from Yambo)!
Éireann go Brách