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 zdirection 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 nondeformed 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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 Spring '11
 Sigrist
 Electron, Magnetic Field, Fundamental physics concepts, Condensed matter physics

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