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Unformatted text preview: B . The linearized Boltzmann equation in this case reads-e v k · E ∂f ( ε k ) ∂ε k =-g ( k ) τ ( ε k ) + e ~ ( v k × B ) ∂g ( k ) ∂ k (2) where g ( k ) = f ( k )-f ( k ). a) Why is in (2) the magnetic ﬁeld in ﬁrst order not a driving ﬁeld, contrary to the electric ﬁeld? b) Calculate for the case of B = (0 , ,B ) the resistivity tensor ˆ ρ = ˆ σ-1 and show that (i) the Hall resistance becomes independent of the scattering time τ and that (ii) the transverse magnetoresistance deﬁned by Δ ρ xx ( B ) = ρ xx ( B )-ρ xx (0) (3) is equal to zero. Hint: Consider independently the cases where the electric ﬁeld points in the x , y and z direction, respectively, and use the ansatz g ( k ) = ak x + bk y . (4) Oﬃce hour: Monday, May 23th, 2011 - 9:00 to 11:00 am HIT K 31.3 Tama Ma...
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This note was uploaded on 10/04/2011 for the course PHYS fs11 taught by Professor Sigrist during the Spring '11 term at Swiss Federal Institute of Technology Zurich.
- Spring '11