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2009.04.24-ECE659-L39-notes

2009.04.24-ECE659-L39-notes - ECE 659 Quantum Transport...

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ECE 659 Quantum Transport: Atom to Transistor Lecture 39: Singlet/Triplet States II 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 No. of Electrons Size of Hamiltonian 0 1x1 1 4x4 2 6x4 3 4x4 4 1x1 a b a b a t b t H a t b t ε = 2 electron subspace: aa bb ab ba ab ab aa bb ab ba ab ab 2 U + 2 U + 2 2 2 2 t t t t t t t t
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For 2 electrons the eigen energies are: 2 ε 2 U + ab ab 2 ab ba - ( 29 * 2 ab ba aa bb + + + 2 - ∆ 2 U + + ∆ ( 29 ( 29 ( 29 1 1 2 2 a b a b aa bb ba ab + + = + + + We see from the multi-electron picture that and terms get de-emphasized, which is not clear from MO theory. If ‘t’ is large, we can work with MO theory and factorize the wavefunction. If ‘t’ is small this is not possible. bb aa In general we can us ‘Schrodinger Eqn.’ for the complete system: i H t ψ = H is the Hamiltonian for the complete system 2 Lowest energy states: Molecular Orbital Theory: a a b b , 2 2 a b a b - - , 2 2 a b a b + + Now, ( 29 1 i i B E N k T i P e Z μ - -
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2009.04.24-ECE659-L39-notes - ECE 659 Quantum Transport...

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