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2009.02.20-ECE659-L17-notes

# 2009.02.20-ECE659-L17-notes - = Σ = Total current in n op...

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ECE 659 Quantum Transport: Atom to Transistor Lecture 17: Non-Coherent Transport Supriyo Datta Spring 2009 Notes prepared by Samiran Ganguly

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H 1 Σ 2 Σ 1 μ 2 [ ] v 1 1 2 2 1 n in f f i G EI H G G G A i G G G G G G + - + Γ + + + Γ = Σ - Σ = - - Σ = Σ = - = Γ = Γ 2 n G πψψ + = get total current we need to take the Trace of 2 in ss E H s π ψ + Σ = = + Σ + Φ dhhDhh± op I i + + Φ - Φ = d i dt = Φ ɶ ɶ current ( 29 d dt ψψ + ɶ ɶ To get total current we need to take the Trace of I op V V 1 2 1 0 n n op n n G G H H Trace I Trace i Trace HG G H ih + + - = = - =
ψ Φ = Σ 2 1 1 op n n op n n op I i Trace I Trace G G ih Trace G ih Trace G Trace I h ψψ π + + + + + Σ - Σ = = Σ - Σ = Σ - Σ - Γ = ( 29 in in op in in G G Trace I Trace ih Trace G G ih Trace A h + + Σ - Σ = Σ -

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Unformatted text preview: = Σ = Total current: in n op Trace A G Trace I h Σ-Γ = s Φ = op s s I i + +-= ℏ Gs = v 2 in op ss G Gss I i + + + Σ-= ℏ 1 2 1 1 2 2 in f f Γ = Γ + Γ Σ = Γ + Γ For current at each terminal we can use the subscripted expression: ( 29 in n m m m n m m m q I Trace A G h q I Trace Af G h = Σ- Γ = Γ- Scatterer 2 scatterer (calculated) 1 Σ 2 Σ 1 μ 2 ε t Ballistic 1 scatterer 2 scatterer (expected)...
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2009.02.20-ECE659-L17-notes - = Σ = Total current in n op...

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