Page 110 - Principles and Applications of NanoMEMS Physics

98 Chapter 3

G
f s a , = 2 L + 1 ³ d 2 ΩP (cos θ )f s a , ( kk , G ) ′ , (53)
L 4π L

which in normalized form are rewritten as,

F a s , = k F m * f a s , . (54)
π
L 2 L

Following the considerations in the discussion of the noninteracting electron
gas, excitations of the Fermi liquid are also captured by the specific heat and
the magnetic susceptibility. These calculations assume that, for low energies,
E → E and m → m *, and yield [133],
0
k k

γ = m * k F k B 2 , (55)
3

and

2
χ = 1 ⋅ µ k F m * (56)
B
1 + F a π 2
0
from where the Wilson ratio is given by (57) in terms of the Landau
a
parameter F .
0

R = 1 . (57)
1+ F
W a
0
For the quintessential example of a Fermi liquid, namely, liquid helium 3
3
( He ), a coefficient of F a ≈ − 7 . 0 [133] was obtained experimentally,
0
resulting in a Wilson ratio R ≈ . 3 33 , which denotes strong interaction.
W
Landau’s Fermi liquid theory succeeds in capturing the phenomenology of
near equilibrium properties, as shown above, however, in situations when it
is not possible to write a simple expansion for f, as is the case in highly
anisotropic metals, the application of the theory to obtain quantitative results
becomes impossible [133], [134].
A more fundamental limitation of the theory derives from the
circumstances under which the concept of quasi-particles is valid, namely,
when their lifetime is longer than the time it takes to turn on the interaction
[133], [134]. In particular, if the Hamiltonian for the interacting system as a