2009.03.11-ECE659-L24-notes

2009.03.11-ECE659-L24-notes - ECE 659 Quantum Transport:...

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Unformatted text preview: ECE 659 Quantum Transport: Atom Atom to Transistor Lecture 24: Spin Supriyo Datta Spring 2009 Notes prepared by Samiran Ganguly I u d 2q γ 1γ 2 ℏ γ1 + γ 2 V γ1 γ2 µ1 µ2 0 ε 0 i γ i γ H = Σ1 = − 1 Σ2 = − 2 2 0 γ2 20 0 ε 0 γ1 Magnetoresistive device: q α 2 β 2 q α + β IP = + = ℏ 2α 2 β ℏ 2 q 2αβ I AP = ℏα +β α B α α β I P (α + β ) = 4αβ I AP I P − I AP (α − β ) = I AP 4αβ 2 2 β β β α GMR Device: metal between the contacts TMR Device: oxide between contacts z E y x Polarizer Analyzer Eletro-optic modulator Spinors: In 3-D: Vectors: z : cos θ x : sin θ up : cos θ down : sin θ Vectors: 2 2 z : cos θ x : sin θ cos φ y : sin θ sin φ Spinors: up : cos θ e 2 − iφ 2 down : sin θ e 2 + iφ 2 α Σ= 0 0 β if we use +x and –x as basis We have to transform from x to z basis: So: ˆ ˆ x −x Σ= ˆ z ˆ −z ˆ x α × −x 0 ˆ ˆ ˆ x −x ˆ ˆ z −z Σ= ˆ 0 x × β −x ˆ 1 1 1 α 0 1 1 2 1 −1 0 β 1 −1 1 α + β α − β = 2 α − β α + β ...
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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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2009.03.11-ECE659-L24-notes - ECE 659 Quantum Transport:...

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