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

CQT Lecture #1 nano HUB .org online simulations and more Unified Model for CQT, Lecture#1: Quantum Transport Nanodevices and Maxwell’s Far from Equilibrium Demon Σ s Objective: To illustrate the subtle interplay of dynamics and thermodynamics μ 1 μ 2 H that distinguishes transport physics. Σ 1 Σ 2 Reference: S.Datta,"Nanodevices and Maxwell's demon", to appear in the Proceedings of the Third ASI International “QTAT” Workshop on Nano Science & Datta, Quantum Transport: Technology, Ed. Z.K.Tang, Taylor & Atom to Transistor, Francis (2007). Cambridge (2005) http://arxiv.org/abs/0704.1623 Supriyo Datta 1 Network for Computational Nanotechnology

Maxwell’s demon nano HUB .org online simulations and more Electronic demon <---- L ----> Channel Drain Source ---- V = 0 V I Supriyo Datta 2 Network for Computational Nanotechnology

Top-down view nano HUB .org online simulations and more V = I R or I = V G <---- L ----> Channel Source Drain Conductance, G = 1/ R = σ I V G A / L Conductivity σ = 2 τ q n / m CHANNEL m = ? n = ? τ = ? “Very complicated” Supriyo Datta 3 Network for Computational Nanotechnology

Bottom-Up View nano HUB .org online simulations and more “Top” Bottom-up View Ohm’s law <---- L ----> = = σ I GV , G A / L Source Channel Drain Escape rate I V Density of states γ ≡ escape rate = ( 2 π D γ G q / h ) ( ) CHANNEL = 2 G ( q / h ) � � � “Bottom” Ω 1 / 25 . 8 K Supriyo Datta 4 Network for Computational Nanotechnology

Equilibrium Energy Level Diagram nano HUB .org online simulations and more V G < 0 V G “Gate” Vacuum V G > 0 Level S Channel D EMPTY Insulator µ No states V FILLED Electrochemical S Channel D Potential Supriyo Datta 5 Network for Computational Nanotechnology

What makes electrons flow? nano HUB .org online simulations and more S Channel D V µ 1 µ 1 µ 2 µ 2 I I V V Supriyo Datta 6 Network for Computational Nanotechnology

Escape rate nano HUB .org online simulations and more γ 2 / � Current depends on γ � / 1 Density of states, D(E) µ 1 around the contact electrochemical qV potentials. µ 2 AND on escape rates γ γ γ / � : Escape Rate 1 2 γ has dimensions of energy Supriyo Datta 7 Network for Computational Nanotechnology

Where is the power dissipated ? nano HUB .org online simulations and more γ γ Power = V I qV { <---- L ----> γ γ Channel D(E) Drain Source V I Dissipation Dissipation Contacts assumed Newton’s law to remain in equilibrium Schrodinger equation Thermodynamics Dynamics Supriyo Datta 8 Network for Computational Nanotechnology

Dynamics and dissipation nano HUB .org online simulations and more Separate dynamics Dissipation Dissipation + dissipation γ γ Dynamics Landauer { } model Newton’s law Schrodinger equation Mixed dynamics γ + dissipation γ γ s Boltzmann NEGF Supriyo Datta 9 Network for Computational Nanotechnology

Spin Valves nano HUB .org online simulations and more Anti-parallel (AP) Drain Channel Source Insulating substrate Imperfect Current Source AP Perfect AP Drain Voltage V Supriyo Datta 10 Network for Computational Nanotechnology

Perfect AP with Spin-flip Impurities nano HUB .org online simulations and more Spin flip Channel Source Drain - + Insulating substrate Source Drain Spin Current flip with spin-flip w/o spin-flip + - Voltage Source Drain Supriyo Datta 11 Network for Computational Nanotechnology

Perfect AP with Spin-polarized gate nano HUB .org online simulations and more Spin flip Channel Source Drain Insulating substrate - + Source Drain Spin Current flip + - Voltage Source Drain Supriyo Datta 12 Network for Computational Nanotechnology

Current at zero voltage ! ! nano HUB .org online simulations and more 1 Normalized current ---> Channel Source 0.5 Drain 0 -0.5 Current -1 -0.1 -0.05 0 0.05 0.1 Voltage ---> Fig : 1A Voltage Supriyo Datta 13 Network for Computational Nanotechnology

Device to “demon” nano HUB .org online simulations and more 1 Normalized current ---> 0.5 0 Drain Source Channel -0.5 -1 -0.1 -0.05 0 0.05 0.1 Voltage ---> No further current Supriyo Datta 14 Network for Computational Nanotechnology

Where did the energy come from? nano HUB .org online simulations and more Channel Source Drain Drain Channel Source Answer: From the contacts Supriyo Datta 15 Network for Computational Nanotechnology

Second law ? nano HUB .org online simulations and more Channel Source Drain Drain Channel Source S = k ln W S = 0 S = Nk ln 2 Energy upto may be extracted T Δ S Supriyo Datta 16 Network for Computational Nanotechnology

Resetting the demon takes energy nano HUB .org online simulations and more No energy needed Source Drain Channel Drain Channel Source Need > N kT to “Erase” Maxwell’s demon, ed. H.S.Leff and A.F.Rex, ISBN 0-691-08727-X pbk Supriyo Datta 17 Network for Computational Nanotechnology

Nanomagnets : Bistable demons nano HUB .org online simulations and more 1 .. A finite-sized 0.9 Higher energy 0.8 Energy demon .. gets so 0.7 Normalized Energy hot that he cannot 0.6 see very well after 0.5 0.4 a while ..”, 0.3 Feynman lectures, 0.2 Vol.1, 46-5. 0.1 0 0 50 100 150 200 250 300 350 Angle of magnetization from plane of magnet Flipping a spin costs energy Supriyo Datta 18 Network for Computational Nanotechnology

The cool demon as a heat engine nano HUB .org online simulations and more 0.25 Cooled 0.2 T D > - 0.15 T D = 60K - - 0.1 t 0.05 n e 0 r r -0.05 u T D = 300K C -0.1 Q 1 : heat from contacts -0.15 Q 2 : heat to demon -0.2 Channel T D = 600K Source Drain -0.25 Q 1 - Q 2 : useful work -0.05 0 0.05 300K 300K Voltage ---> Carnot’s Q 1 Q 2 < principle kT kT D Supriyo Datta 19 Network for Computational Nanotechnology

Cooling the demon: Refrigerator nano HUB .org online simulations and more T D Cooled Heat from by device surroundings Q 1 : heat delivered to contacts Q 2 : heat taken from demon Channel Source Drain 300K 300K Battery delivers Q 1 - Q 2 Carnot’s Q 1 Q 2 > principle kT kT D Supriyo Datta 20 Network for Computational Nanotechnology

Why is the flow unidirectional ? nano HUB .org online simulations and more S = Nk ln 2 S = 0 No energy needed Source Drain Channel Drain Channel Source Need > N kT to “Erase” Supriyo Datta 21 Network for Computational Nanotechnology

Entropy as a driving force nano HUB .org online simulations and more All “blue” Drain Channel Source Supriyo Datta 22 Network for Computational Nanotechnology

Entropy-driven vs. dynamic processes nano HUB .org online simulations and more Down > Up “Reservoir” “System” E Σ s μ 1 μ 2 H Density of states Σ 1 Σ 2 Supriyo Datta 23 Network for Computational Nanotechnology

Entangled “demon” nano HUB .org online simulations and more Entangled ! + * B * A Source Drain Channel A 2 B 2 Supriyo Datta 24 Network for Computational Nanotechnology

Unified model for nanodevices nano HUB .org online simulations and more Macroscopic “Even simple things .. work .. in only one 0.1 dimensions direction because it has some ultimate mm contact with the rest of the universe ..” <--- L --> Feynman lectures, Vol.1, 46-8 10 µm Diffusion 1 µ m Hot Σ s Boltzmann 0.1 µm μ 1 μ 2 H 10 nm + “Landauer” = 1 nm Σ 1 Σ 2 “NEGF” 0.1 nm Atomic Nanowires, nanotubes, molecules ….. dimensions Switches, energy conversion … Supriyo Datta 25 Network for Computational Nanotechnology