2009.04.27-ECE659-L40-notes

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

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Unformatted text preview: ECE 659 Quantum Transport: Atom Atom to Transistor Lecture 40: Correlated Transport Supriyo Datta Spring 2009 Notes prepared by Samiran Ganguly aa H +U Σ2 ε1 a a 2ε1 + U t b b a a 0 ε1 0 Σs ε2 Σ1 aa bb 2ε 2 + U t t ab t t ba t t ab ab abab a ε1 t b t ε1 H= ε2 t a t ε2 b aa bb ab ba ab 2ε1 + U t t ε1 + ε 2 ε1 + ε 2 ε1 + ε 2 ε1 + ε 2 ab ρ= H − µN 1 exp − Z k BT Z = Trace ( ρ ) Single Level: I= γ1 q γ 1γ 2 ℏ γ1 + γ 2 P0 = P0 = 1 1 + γ1 γ 2 I γ2 a V γ1 γ 2 1 + γ1 γ 2 q γ 1γ 2 ∴I = ℏ γ1 + γ 2 Two Levels: q 2γ 1γ 2 ℏ γ1 + γ 2 a γ 1 f1 +γ 2 f 2 P 1 γ 1 f1 +γ 2 f 2 P γ 1 f1 + γ 2 f 2 1 = P0 γ 1 f1 + γ 2 f 2 f = f E−µ = exp − k BT I a P 0 q 2γ 1γ 2 ℏ 2γ 1 + γ 2 Maximum current: f1 = 1, f 2 = 0 V P γ1 1 = P0 γ 2 I = q P0 ℏ γ1 a a a a aa 2ε1 +U γ1′ b a γ1 γ2 0 a ε1 0 γ1 γ1 a γ2 Pa γ 1 Pa = = P0 γ 2 P0 Pa + Pa 2γ 1 = P0 γ2 P0 = 1 1 + 2γ 1 γ 2 2γ 1 γ 2 1 + 2γ 1 γ 2 b ε1 a ε2 γ1 γ2 0 γ 1′ 0 I Pa + Pa = I= q γ 1γ 2 ℏ γ1 + γ 2 q q 2γ 1γ 2 2γ 1 P0 = ℏ ℏ 2γ 1 + γ 2 V Once ‘b’ is filled it charges the channel so much that the ‘a’ level floats up too high making the current go to 0 Singlet and Triplet: ε1 a a t b b ε2 abab a ε1 t b t ε1 H= ε2 t a t ε2 b (**) a + b (**) a + b Singlet State ab + ba + (*) aa + (*) bb If we pull out b, the conduction can occur because we are left with a & b Triplet State T S 1e − ...
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This note was uploaded on 01/30/2011 for the course ECE 659 taught by Professor Staff during the Spring '08 term at Purdue University-West Lafayette.

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

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