Maxwells demon nano HUB .org online simulations and more Electronic - - PowerPoint PPT Presentation

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H

Σ1

Σ2

μ1 μ2

Σs

CQT Lecture #1

Unified Model for Quantum Transport Far from Equilibrium

CQT, Lecture#1:

Nanodevices and Maxwell’s Demon

Objective: To illustrate the subtle interplay of dynamics and thermodynamics that distinguishes transport physics. Reference: S.Datta,"Nanodevices and Maxwell's demon", to appear in the Proceedings

• f the Third ASI International

Workshop on Nano Science & Technology, Ed. Z.K.Tang, Taylor & Francis (2007).

http://arxiv.org/abs/0704.1623

“QTAT” Datta, Quantum Transport: Atom to Transistor, Cambridge (2005)

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Maxwell’s demon

Channel Source Drain

V I

<---- L ---->

Electronic demon

• V = 0

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Top-down view

CHANNEL

V = I R or I = V G Conductance, G = 1/ R

L A G / σ =

Conductivity

m n q /

2

τ σ =

? = τ

“Very complicated”

m = ? n = ?

I V

Channel Drain <---- L ----> Source

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Bottom-up View Ohm’s law

L A G GV I / , σ = =

CHANNEL

• Ω

=

K

h q G

8 . 25 / 1 2

) / (

rate escape ≡ γ “Bottom” “Top” Bottom-Up View

Channel Source Drain

I V

<---- L ---->

) ( ) / ( 2 γ π D h q G =

Density of states Escape rate

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S Channel D

V

Equilibrium Energy Level Diagram

Vacuum Level

Electrochemical Potential

µ

S Channel D

VG > 0 VG < 0

No states

FILLED EMPTY

Insulator

VG “Gate”

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What makes electrons flow?

µ2 µ1

V I

µ1 µ2

I V

S Channel D

V

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Escape rate

Rate Escape : / γ

has dimensions of energy γ

• /

1

γ

γ2 /

µ1

qV

µ2

Current depends on Density of states, D(E) around the contact electrochemical potentials.

2

γ

1

γ

AND

• n escape rates

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Where is the power dissipated ?

Power = V I

γ γ

{ qV

Dissipation Dissipation Dynamics

Newton’s law Schrodinger equation

Thermodynamics

Contacts assumed to remain in equilibrium

γ γ

D(E)

Channel Source Drain

V I

<---- L ---->

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Dynamics and dissipation

γ γ

s

γ

γ γ

} {

Dynamics Newton’s law Schrodinger equation Dissipation Dissipation Landauer model Boltzmann NEGF

Mixed dynamics + dissipation Separate dynamics + dissipation

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Spin Valves

Insulating substrate Channel Source Drain

Anti-parallel (AP) Imperfect AP Current Voltage Perfect AP Source Drain

V

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Perfect AP with Spin-flip Impurities Current Voltage

w/o spin-flip with spin-flip

Insulating substrate Channel Source Drain

Drain Source

+

• Spin

flip Drain Source

• +

Spin flip

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Perfect AP with Spin-polarized gate

Insulating substrate Channel Source Drain

Voltage

Spin flip Drain Source

+

• Spin

flip Drain Source

• +

Current

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Current at zero voltage ! !

Channel Source Drain

Current Voltage

• 0.1
• 0.05

0.05 0.1

• 1
• 0.5

0.5 1

Normalized current ---> Voltage --->

Fig : 1A

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Device to “demon”

Channel Source Drain

• 0.1
• 0.05

0.05 0.1

• 1
• 0.5

0.5 1

Normalized current ---> Voltage --->

No further current

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Where did the energy come from?

Channel Source Drain Channel Source Drain

Answer: From the contacts

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Second law ?

Channel Source Drain Channel Source Drain

S = 0 S = Nk ln 2

Energy upto may be extracted

T ΔS

S = k ln W

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Resetting the demon takes energy

Channel Source Drain Channel Source Drain

Need > N kT to “Erase” No energy needed

Maxwell’s demon, ed. H.S.Leff and A.F.Rex, ISBN 0-691-08727-X pbk

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Nanomagnets : Bistable demons

50 100 150 200 250 300 350 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Angle of magnetization from plane of magnet Normalized Energy

Flipping a spin costs energy .. A finite-sized demon .. gets so hot that he cannot see very well after a while ..”, Feynman lectures, Vol.1, 46-5. Energy Higher energy

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The cool demon as a heat engine

• 0.05

0.05

• 0.25
• 0.2
• 0.15
• 0.1
• 0.05

0.05 0.1 0.15 0.2 0.25

TD = 60K TD = 600K TD = 300K

Voltage ---> C u r r e n t

• >

TD

Channel Source Drain 300K 300K

Q1 kT < Q2 kTD

Carnot’s principle Cooled Q1: heat from contacts Q2: heat to demon Q1 - Q2 : useful work

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Cooling the demon: Refrigerator

Q1 kT > Q2 kTD

TD

Channel Source Drain 300K 300K

Q1: heat delivered to contacts Q2: heat taken from demon Battery delivers Q1 - Q2

Heat from surroundings Cooled by device

Carnot’s principle

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Why is the flow unidirectional ?

Channel Source Drain Channel Source Drain

Need > N kT to “Erase” No energy needed S = 0 S = Nk ln 2

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Entropy as a driving force

All “blue”

Channel Source Drain

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Entropy-driven vs. dynamic processes E Density

• f states

“Reservoir”

Down > Up

“System” H

Σ1

Σ2

μ1 μ2

Σs

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Entangled “demon”

Channel Drain Source

* A * B

+

Entangled ! A2 B2

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Unified model for nanodevices

Diffusion Boltzmann “NEGF”

<--- L -->

0.1 mm 10 µm 1 µ m 0.1 µm 10 nm 1 nm 0.1 nm

Macroscopic dimensions Atomic dimensions

H

Σ1

Σ2

μ1 μ2

Σs

+ “Landauer” =

“Even simple things .. work .. in only one direction because it has some ultimate contact with the rest of the universe ..” Feynman lectures, Vol.1, 46-8

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