cqt-datta-l4-slides

# cqt-datta-l4-slides - nanoHUB.org online simulations and...

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nano HUB .org Supriyo Datta 1 online simulations and more Network for Computational Nanotechnology CQT Lecture #4 Unified Model for Quantum Transport Far from Equilibrium CQT, Lecture#4: Coulomb blockade and Fock space Objective: To illustrate the limitations of the model described in Lectures 2,3 and introduce a completely different approach based on the concept of Fock space. I believe this will be a key concept in the next stage of development of transport physics. Approach based on (1)Beenakker, Phys.Rev.B44,1646 (1991), (2) Averin & Likharev, J.LowTemp.Phys. 62, 345 (1986) Reference: QTAT, Chapter 3.4. “QTAT” Datta, Quantum Transport: Atom to Transistor, Cambridge (2005) U: Self-consistent Field (SCF) H Σ 1 Σ 2 μ 1 2 Σ s

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nano HUB .org Supriyo Datta 2 online simulations and more Network for Computational Nanotechnology Current through a very small conductor I = q = γ 1 2 1 + 2 f 1 f 2 [] F = 1 f 1 + 2 f 2 1 + 2 = / 1 γ 2 / = μ 1 2 = / 1 γ 2 / = 1 2 -0.2 0 0.2 0.4 0.6 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 N o r m a li z ed C u en t qV D max I = q = 1 2 1 + 2 q 1 2 = if 2 = 1 q 1 2 = = / 1 γ 2 / = 1 2 = / 1 γ 2 / = 1 2 F 1 f
nano HUB .org Supriyo Datta 3 online simulations and more Network for Computational Nanotechnology Conductance of a very small conductor = / 1 γ γ 2 / = μ 1 2 = / 1 γ 2 / = 1 2 N o r m a li z ed C u en t Assume 2 = γ 1 -0.2 0 0.2 0.4 0.6 0.8 -0.2 0 0.2 0.4 0.6 0.8 1 q 1 2 = T k B 4 qV D Conduc tan ce = I V D ~ q 1 /2 = 2 1 + 4 k B T ~ q 2 /4 = if 1 >> k B T Conduc tan ce quantum ~ q 2 π = = / 1 γ 2 / = 1 2 + 1 2

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nano HUB .org Supriyo Datta 4 online simulations and more Network for Computational Nanotechnology Effect of “U” on conductance V G V D CHANNEL D S I = / 1 γ γ 2 / = μ 1 2 = / 1 γ 2 / = 1 2 N o r m a li z ed C u en t -0.2 0 0.2 0.4 0.6 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 qV D q 1 2 = U 0 /2 Assume U 0 >> k B T , 1 , 2 Level floats up by U 0 2 1 + γ 2 U 0 : Increase in potential due to SINGLE electron Assume 2 = γ 1 U 0 = 0.5 eV
nano HUB .org Supriyo Datta 5 online simulations and more Network for Computational Nanotechnology SCF with self-interaction correction V G V D CHANNEL D S I = / 1 γ γ 2 / = μ 1 2 = / 1 γ 2 / = 1 N o r m a li z ed C u en t -0.2 0 0.2 0.4 0.6 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 qV D q 1 2 = U 0 /2 Level does NOT float up Assume 2 = γ 1 U 0 = 0.5 eV U i = U 0 ( N N i ) Self-interaction Correction

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nano HUB .org Supriyo Datta 6 online simulations and more Network for Computational Nanotechnology -0.2 0 0.2 0.4 0.6 0.8 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 2 levels: Unrestricted SCF = / 1 γ γ 2 / = μ 1 2 = / 1 γ 2 / = 1 2 U i = U 0 ( N N i ) Self-interaction Correction U i = U 0 N Restricted SCF Unrestricted SCF = / 1 γ 2 / = 1 2
nano HUB .org Supriyo Datta 7

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## This note was uploaded on 12/30/2010 for the course EE 495 taught by Professor S.datta during the Spring '10 term at Purdue University Calumet.

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cqt-datta-l4-slides - nanoHUB.org online simulations and...

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