2009.03.25-ECE659-L27-notes

2009.03.25-ECE659-L27-notes - ECE 659 Quantum Transport...

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ECE 659 Quantum Transport: Atom to Transistor Lecture 27: Spin Orbit Interaction Supriyo Datta Spring 2009 Notes prepared by Samiran Ganguly
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H s Σ 2 Σ 1 Σ V 1 μ 2 2 p p i qV t m ψ = - a a ɶ ɶ 0 1 1 0 x σ = 0 0 y i i - = 1 0 0 1 z = - With spin p i = - ∇ a If we have a magnetic field in z direction Schrodinger Equation is given by: { } { } { } 0 1 0 0 0 1 2 B z H i B H t p p H qV m = + - = - a a Magnetic field in x direction introduces a coupling: { } 0 1 1 0 B x B In a concise way: B B μ σ a a 0 1 0 1 0 1 0 0 0 1 x x y y z z x y z B B B B i B B B i = + + - = + + - a a Where: Schrodinger Equation becomes: { } { } { } 0 0 B H i B H t = + a a
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2009.03.25-ECE659-L27-notes - ECE 659 Quantum Transport...

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