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2009.04.27-ECE659-L40-notes

2009.04.27-ECE659-L40-notes - ECE 659 Quantum Transport...

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ECE 659 Quantum Transport: Atom to Transistor Lecture 40: Correlated Transport SupriyoDatta Spring 2009 Notes prepared by SamiranGanguly
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H U s Σ 2 Σ 1 Σ a a b b t 1 ε 2 ε aa bb ab ba ab ab aa 1 2 U ε t t a b a b 1 ε 0 aa 1 2 U ε a a 0 bb ab ba ab ab 1 2 ε ε t t t t t t 1 1 2 2 t a t b H t a t b ε ε ε ε = 2 2 U ε 1 2 ε ε 1 2 ε ε 1 2 ε ε ( 29 1 exp B H N Z k T Z Trace μ ρ ρ - = - =
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Single Level: 1 γ 2 γ a I V 1 2 1 2 q I γ γ γ γ = 1 1 1 2 2 0 1 1 2 2 P f f P f f f γ γ γ γ + = + = 0 1 2 1 2 0 1 2 1 2 1 2 1 1 1 P P q I γ γ γ γ γ γ γ γ γ γ = + = + = Two Levels: I 1 2 2 q γ γ γ γ 1 P 1 1 f f γ γ 1 1 f f γ γ a exp B f E k T μ - = - Maximum current: 1 2 1, 0 f f = = 1 1 0 2 1 0 P P I q P γ γ γ = = V 1 2 1 2 1 2 2 2 q γ γ γ γ 0 P 2 2 2 2 a a a a a
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1 ε 0 aa 1 2 U ε a a 0 1 γ 1 γ 2 γ 1 0 2 0 1 2 a a a a P P P P P P P γ γ γ γ = = + = 1 γ 2 γ a b 1 γ 1 ε 0 b a 0 1 γ 1 γ 2 γ 2 ε 0 2 0 1 2 1 2 1 2 1 2 1 0 1 2 1 1 2 2 1 2 2 2 2 a a P P P q q I P γ γ γ γ γ γ γ γ γ γ γ = + + = + = = I V 1 2 1 2 q γ γ γ γ Once ‘b’ is filled it charges the channel so much that the ‘a’ level floats up too high making the current go to 0
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