2009.04.03-ECE659-L31-notes

2009.04.03-ECE659-L3 - ECE 659 Quantum Transport Atom Atom to Transistor Lecture 31 Spin Current/Torque Supriyo Datta Spring 2009 Notes prepared by

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ECE 659 Quantum Transport: Atom to Transistor Lecture 31: Spin Current/Torque Supriyo Datta Spring 2009 Notes prepared by Samiran Ganguly
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H 2 Σ 1 Σ s Σ 2 2 n in n n n n in in op a b b a abc c c a b b a ab G G G i I HG G H G G G G i I σ σ ε σ δ + + + = Σ = - + Σ - Σ + Σ - Σ - = + = [ ] [ ] [ ] n x y z G w I x y z = + + + ( 29 n N Trace G = If we have unpolarized spins: 1 1       ( 29 1 1 1 1 1 1 1 1 1 1 2 2   =     ( 29 n z z S Trace G = In general: ( 29 n S Trace G = a a Spin polarizations: 1 0       0 1       ( 29 1 1 0 1 0 0 0 0   =     ( 29 0 0 0 0 1 1 0 1   =     1 2 0 0 1 2 unpolarized: 1 1 - ( 29 1 1 1 1 1 1 1 1 1 1 2 2 - - = - - u d u d u d u d 1 2 1 2
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n G i H s t ψψ ψ + = + Σ + Current: ( 29 i t + ( 29 ( 29 n in op Trace G Trace G G Trace I i i + + Σ - Σ Σ - = + n Trace G Γ in Trace A Σ ( 29 ( 29 ( 29 0 0 1 1 n n n n z z n n z z n z z Trace HG G H i Trace I G G I i Trace G G i Trace G i σ ε εσ σ σ - = + - + = - = -
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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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2009.04.03-ECE659-L3 - ECE 659 Quantum Transport Atom Atom to Transistor Lecture 31 Spin Current/Torque Supriyo Datta Spring 2009 Notes prepared by

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