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ECE495N-F08-HW_7 - ECE 495N Fall08 ME118 MWF 1130A 1220P...

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11/12/08 1 ECE 495N, Fall’08 ME118, MWF 1130A – 1220P HW#7: Due Friday Nov.21 in class. Problem 1: Below is some recent experimental data on a sheet of graphene reported by one of the leading groups in the field ( http://arxiv.org/abs/0805.1830 ). It plots the "conductivity" σ obtained from the conductance G, using the relation G = W / L , W and L being the width and length respectively. We wish to try to understand this data based on the expressions developed in this course (you may want to review Problem 1 of HW#3): 0 [ ( ) ( )] ( ) eq N N dEDE U DE f E +∞ −∞ = −− (1) 2 () eq f q G dEM E U h LE λ λ∂ +∞ −∞  =  +  (2) where is the mean free path and f eq ( E ) = 1 1 + exp( / kT ) .
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11/12/08 2 A. Starting from the approximate dispersion relation () k vk ε , use the relations ( ) ( ( )) k DE E k δε = () ( ) ( ( )) x k vk ME E k L π = to show that 2 2 E LW v = and 4 E W v = including a factor of 2 for the two spins and another factor of 2 for the two valleys.
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ECE495N-F08-HW_7 - ECE 495N Fall08 ME118 MWF 1130A 1220P...

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