ex10 - Solid State Theory Exercise 10 SS 11 Prof M Sigrist...

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Solid State Theory Exercise 10 SS 11 Prof. M. Sigrist Exercise 10.1 Uniaxial Compressibility We consider a system of electrons upon which an uniaxial pressure in z-direction acts. Assume that this pressure causes a deformation of the Fermi surface k k 0 F of the form k F ( φ,θ ) = k 0 F + γ 1 k 0 F h 3 k 2 z - ( k 0 F ) 2 i = k 0 F + γk 0 F [3 cos 2 θ - 1] , (1) where γ = ( P z - P 0 ) /P 0 is the anisotropy of the applied pressure. a) Show that for small γ ± 1, the deformed Fermi surface k F ( φ,θ ) encloses the same volume as the non-deformed one, k 0 F , where terms of order O ( γ 2 ) can be neglected. b) The deformation of the Fermi surface effects a change in the distribution function of the electrons. Using Landau’s Fermi Liquid theory, calculate the uniaxial com- pressibility κ u = 1 V 2 E ∂P 2 z , (2) which is caused by he deformation given in eq. (1) ( E denotes the Landau energy functional). Exercise 10.2 Polarization of a neutral Fermi liquid
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ex10 - Solid State Theory Exercise 10 SS 11 Prof M Sigrist...

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