Paul M. Grant Visiting Scholar, Stanford (2005-2008) IBM Research Staff Member Emeritus EPRI Science...
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![Page 1: Paul M. Grant Visiting Scholar, Stanford (2005-2008) IBM Research Staff Member Emeritus EPRI Science Fellow (Retired) Principal, W2AGZ Technologies The.](https://reader036.fdocuments.in/reader036/viewer/2022062717/56649e355503460f94b23646/html5/thumbnails/1.jpg)
Paul M. GrantVisiting Scholar, Stanford (2005-2008)IBM Research Staff Member Emeritus
EPRI Science Fellow (Retired)Principal, W2AGZ Technologies
The Third International Conference on Quantum, Nano and Micro Technologies
ICQNM 2009 February 1-7, 2009 - Cancun, Mexico
Does the
Hold the Key to Room Temperature Superconductivity?
http://www.w2agz.com/rtsc07.htm
Quasiperiodic Quasi-One-Dimensional Metallic Nano-Structures
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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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NanoConstruct
“Eigler Derricks”
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(((
Models of Electrical Conductivity1900
One Idea:R
T
Just Goesto Zero!
(((
(((
(((
• •e-e-
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The Most Popular:R
T
Freezes Out!e-
Models of Electrical Conductivity1910
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Thus the mercury at 4.2 K has entered a new state, which, owing to its particular electrical properties, can be called the state of superconductivity
H. Kamerlingh-Onnes (1911)
1911: A Big Surprise!
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Physics of Superconductivity(Carriers Pair Off)
+ +
+ +•e-
•e-
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1
*CT a e
“Bardeen-Cooper-Schrieffer”
Where
= Debye Temperature (~ 275 K)
= 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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Electron-Phonon Coupling a la Migdal-Eliashberg-McMillan
(plus Allen & Dynes)
First compute this via DFT…
Then this…
Quantum-Espresso (Democritos-ISSA-CNR)
http://www.pwscf.org Grazie!
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“3-D”AluminumTC = 1.15 K
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1986: Another Big Surprise!
Bednorz and MuellerIBM Zuerich, 1986
1980 2000
Hig
h-T
C
164 K
La-214
Hg-1223
V3Si
1900 1920 1940 1960 0
50
100
150
200
Tem
per
atu
re,
TC
(K)
Year
Low-TCHg
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Diethyl-cyanine iodide
Little, 1963
+
+
+
+
+
+-
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-
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1
*CT a e
“Bill Little’s BCS”
Where
= Exciton Characteristic Temperature (~ 22,000 K)
= Fermion-Boson Coupling Constant (~ 0.2)
* = Fermion-Fermion Repulsion (?)
a = “Gap Parameter, ~ 1-3”
Tc = Critical Temperature, ~ 300 K
Fk E
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Allender-Bray-Bardeen (1973)
μ*
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Davis – Gutfreund – Little (1975)
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Al Chain Supercell:c* = c, a*, b* ~ 3 x c*
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Al Chain Supercell:c* = c, a*, b* = >10 x a
• Periodic Al chain unstable – dimerizes!
• Fermi surface is totally gapped!
• However…
…could still give a BCS HTSC if hω >> !
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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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APF “Band Structure”“Electronic Structure of Disordered Solids and Almost Periodic
Functions,”
P. M. Grant, BAPS 18, 333 (1973, San Diego)
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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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Al Fibonacci Chain Supercell:c* = G3(2.862|4.058), a*, b* ~ 2 x c*
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64 = 65
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