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

NanoConcept

What novel atomic/molecular arrangement might give rise to higher temperature superconductivity >> 165 K?

• 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

NanoConstruct

“Eigler Derricks”

(((

Models of Electrical Conductivity1900

One Idea:R

T

Just Goesto Zero!

(((

(((

(((

• •e-e-

The Most Popular:R

T

Freezes Out!e-

Models of Electrical Conductivity1910

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!

Physics of Superconductivity(Carriers Pair Off)

+ +

+ +•e-

•e-

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

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!

“3-D”AluminumTC = 1.15 K

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

Diethyl-cyanine iodide

Little, 1963

+

+

+

+

+

+-

-

-

-

-

-

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

Allender-Bray-Bardeen (1973)

μ*

Davis – Gutfreund – Little (1975)

Al Chain Supercell:c* = c, a*, b* ~ 3 x c*

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 >> !

“Not So Famous Danish Kid Brother”

Harald BohrSilver Medal, Danish Football Team, 1908 Olympic Games

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)

APF “Band Structure”“Electronic Structure of Disordered Solids and Almost Periodic

Functions,”

P. M. Grant, BAPS 18, 333 (1973, San Diego)

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)

Al Fibonacci Chain Supercell:c* = G3(2.862|4.058), a*, b* ~ 2 x c*

64 = 65

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