2009.04.29-ECE659-L41-notes

2009.04.29-ECE659-L41-notes - ECE 659 Quantum Transport:...

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ECE 659 Quantum Transport: Atom to Transistor Lecture 41: Exchange Interaction Supriyo Datta Spring 2009 Notes prepared by Samiran Ganguly
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H U + s Σ 2 Σ 1 Σ a a b b t 1 ε 2 a b a b I N+1 1 1 2 2 t a t b H t a t b = V If orbitals are on the different atoms : anti-parallel If orbitals are on the same atom: parallel ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 * * * * a r b r r a r a r b r b r ψ ρ = + = + ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 1 2 1 1 2 2 2 2 1 1 * * * * * * * ab a r b r a r a r b r b r a r a r b r b r b r b r a r a r ψ ψ + N
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Correct form: ( 29 ( 29 ( 29 ( 29 1 2 2 1 1 2 a r b r a r b r ψ = - ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 1 1 2 2 2 2 1 1 1 1 2 2 2 2 1 1 * * * * 1 * 2 * * * * a r a r b r b r a r a r b r b r a r b r b r a r a r b r b r a r ψ ψ + = -
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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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2009.04.29-ECE659-L41-notes - ECE 659 Quantum Transport:...

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