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Unformatted text preview: B . The linearized Boltzmann equation in this case readse v k Â· E âˆ‚f ( Îµ k ) âˆ‚Îµ k =g ( k ) Ï„ ( Îµ k ) + e ~ ( v k Ã— B ) âˆ‚g ( k ) âˆ‚ k (2) where g ( k ) = f ( k )f ( k ). a) Why is in (2) the magnetic ï¬eld in ï¬rst order not a driving ï¬eld, contrary to the electric ï¬eld? b) Calculate for the case of B = (0 , ,B ) the resistivity tensor Ë† Ï = Ë† Ïƒ1 and show that (i) the Hall resistance becomes independent of the scattering time Ï„ and that (ii) the transverse magnetoresistance deï¬ned by Î” Ï xx ( B ) = Ï xx ( B )Ï xx (0) (3) is equal to zero. Hint: Consider independently the cases where the electric ï¬eld points in the x , y and z direction, respectively, and use the ansatz g ( k ) = ak x + bk y . (4) Oï¬ƒce hour: Monday, May 23th, 2011  9:00 to 11:00 am HIT K 31.3 Tama Ma...
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 Spring '11
 Sigrist
 Conductivity, Magnetic Field, Fundamental physics concepts, residual resistivity, conductivity tensor, State Theory Exercise, Prof. M. Sigrist

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