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Unformatted text preview: Solid State Theory Exercise 11 FS 11 Prof. M. Sigrist Transport in metals Exercise 11.1 Relaxation time approximation In this exercise we will show that the socalled singlerelaxationtime approximation, ∂f ( k ) ∂t coll = Z d d k (2 π ) d W ( k , k )[ f ( k ) f ( k )]→  f ( k ) f ( k ) τ , (1) is a true solution to the Boltzmann equation under certain conditions. We consider a homogeneous twodimensional metal with an isotropic Fermi surface ( ε k = ~ 2 k 2 / 2 m ) at zero temperature. The impurity scattering responsible for a finite resistivity is described by a delta potential in real space, V imp ( r ) = V δ ( r ) . (2) The system is subject to a homogeneous and timeindependent electric field along the xaxis. a) Show that the transition rates W ( k , k ) for the impurity potential (2) are constant in kspace. b) Write down the static Boltzmann transport equation for this setup in the form “driftterm” = “collisionintegral” (3) and take advantage of the zerotemperature limit and the symmetries of the system...
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 Spring '11
 Sigrist

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