Page 108 - Principles and Applications of NanoMEMS Physics

96 Chapter 3

On the other hand, the excited particles, while finding themselves at the
G G
same k, k′ as the free elecrons, exhibit a different mass and a different E vs.
G
k relationship than these, in particular, see Figure 3-9, interactions among
the particles with states below E , and between these and the excited
F
electrons with energy above E , are responsible for this. Thus, the
F
dynamical properties of quasi-particles differ from those of free electrons.
Under these circumstances, the theory assumes that for low-energy
excitations, the quasi-particle distribution evolves in such a way that, if
[133],

G
k
n () = 1 if k < k
0 F
G (47)
= 0 if k k < F

(a)
- - -

+ +

(b)
- - -

- - -
- - - - - -
+ + - - -

(c)
Figure 3-9. Fermi liquid representation. (a) Ground state. (b) Excited state. (c) The quasi-
particle exhibits a new effective mass, m*, which derives from its interaction with ground
state electrons as it moves through them. This effective mass is in addition to the mass
derived from its interaction with the crystal lattice (captured by the energy band curvature),
i.e., the dispersion relation E vs. k.

then the distribution of the noninteracting gas is () kn , and, upon excitation
0
n () k → n () k + n δ () k , where δ n () =k + 1 when a quasi-particle is
0 0 G
excited, and () −=kn δ 1 when a quasi-hole is excited. Here, k = ( ),
σ , k