2009.04.08-ECE659-L33-notes

2009.04.08-ECE659-L33-notes - p ikx e ± 2 kL ν π = L sin...

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ECE 659 Quantum Transport: Atom to Transistor Lecture 33: Thermoelectricity Supriyo Datta Spring 2009 Notes prepared by Samiran Ganguly
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H s Σ 2 Σ 1 Σ V 2 μ 1 ( 29 ( 29 1 2 q I dE f f T E h = - An aside on pseudo-spins and graphene: A B x y n ik r A e B       a a k
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( 29 ( 29 ( 29 1 2cos cos 2sin cos x x y x y x y y k a k b B h k t k a k b B σ + = + dhhhDhhh± a dhhhDhhh± ( 29 B x x y y z z H B B B μ = + + Eigenvalues: 2 π θ = Eigenvalues: 2 2 1 2 i i e e φ - + 2sin cos tan 1 2cos cos y x y x x y B k a k b B k a k b = = + Graphene p-n junctions: k n k E 2 2 2 B x y z B B B ± + + z y x 2 2 cos 2 sin 2 i i up e e - + 2 2 sin 2 cos 2 i i down e e - + -
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Unformatted text preview: p ikx e ± 2 kL ν π = L sin kx kL νπ = sin kx solution: ikx ikx e e +- + ( 29( 29 1 2 q I dET E f f h =-∫ ( 29 ( 29 1 1 B E k T f E e μ-= + E f1(E) f2(E) E f1(E) f2(E) 2 1 ( 29( 29( 29 ( 29( 29( 29 1 1 1 2 2 2 1 2 1 1 Q Q I dET E E f f h I dET E E f f h =--=--∫ ∫...
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