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Does the
Hold the Key to Room Temperature Superconductivity?
Paul Michael Grant APS & IOP Senior Life Fellow
IBM Research Staff Member/Manager Emeritus EPRI Science Fellow (Retired) Principal, W2AGZ Technologies
www.w2agz.com
Room 209, Argyros Forum, 9 May 2017, 9:45 AM – 10:30 AM
Superconducting Fluctuations in One-Dimensional Quasi-periodic Metallic Chains
- The Little Model of RTS Embodied -
8 – 9 May 2017
SUPERHYDRIDES
&
MORE
Aging IBM Pensioner (research supported under the IBM retirement fund)
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My Three Career Heroes “Men for All Seasons”
“VL” “Bill” “Ted”
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May, 2028
(still have some time!)
50th Anniversary of Physics Today, May 1998
http://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
= 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”Aluminum,TC = 1.15 K
“Irrational”
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“Put-on !”
Fermion-Boson Interactions
Phonons:
(Al) ~ 430K ~ 0.04eV
Excitons:
(GaAs) ~ 1eV ~ 12,000K
WOW!
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NanoConcept
What novel atomic/molecular
arrangement might give rise
to higher temperature
superconductivity >> 165 K?
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Diethyl-cyanine iodide
Little, 1963
+
+
+
+
+
+ -
-
-
-
-
-
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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• 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 fcc “Dislocation Line”
STO ? SRO !
Al
Al
Al
Al
Al
Al
Al
L = 4.058 Å (fcc edge) s = 2.869 Å (fcc diag)
...or maybe Na on Si?...in other words...”a proxy Little model!”
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64 = 65
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“Not So Famous Danish Kid Brother”
Harald Bohr
Silver Medal, Danish Football Team, 1908 Olympic Games
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Almost Periodic Functions Definition 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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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 Chain Fibo G = 6: s = 2.868 Å, L = 4.058 Å
(a = s+L+s+s = 12.66 Å, b = c ≈ 3×a)
s s s L
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Preliminary 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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What’s Next (1)
- Do a Better Job Computationally - • We now have computational tools (DFT and its
derivatives) to calculate to high precision the ground and
low level exited states of very complex “proxy”
structures.
• In addition, great progress has been made over the past
two decades on the formalism of “response functions,”
e.g., generalized dielectric “constant” models.
• It should now be possible to “marry” these two
developments to predict material conditions necessary to
produce “room temperature superconductivity.
A possible PhD thesis project?
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Davis – Gutfreund – Little (1975)
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What’s Next (2)
- Build It! - • Today we have lots of tools...MBE
(whatever), “printing,” bio-growth...
• So, let’s do it!
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NanoConstruction
“Eigler Derricks”
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h h
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Fast Forward: 2028
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“You can’t always get what you
want…”
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“…you get what you need!”