Page 117 - Principles and Applications of NanoMEMS Physics

3. NANOMEMS PHYSICS: Quantum Wave Phenomena 105

The behavior of the Lüttinger liquid at low energy excitations is captured
by the specific heat and the magnetic susceptibility. The specific heat is
given by,

γ γ = 1 § v F + v F · ¸ , (76)
¨
0 ¨ ¸
2 © u ρ u σ ¹

where γ is the specific heat coefficient for noninteracting electrons at
0
Fermi velocity v , and the spin susceptibility is given by,
F
χ χ = v F . The Wilson ratio is given by [133],
0
u σ
χ γ u 2
R = 0 = ρ . (77)
W γ χ u +
0 ρ u σ

The presentation in this section has exposed the fact that in one-
dimensional transport, the quasi-particles of a Fermi liquid morph into two
new entities, namely, spinons and holons, which, individually, transport spin
and charge, respectively, and characterize the Lüttinger liquid. It will be seen
in the next section, that the manifestation of spin-charge separation is
responsible for a quantitative change in the behavior of 1D TLs.

3.2 Wave Behavior in Periodic and Aperiodic Media

The ability to create patterns of very high precision, made available by
NanoMEMS fabrication technology, will endow engineers with the ability to
effect signal processing on a variety of wave phenomena, e.g., electronic,
electromagnetic, acoustic, etc. Much of this functionality will exploit the
phenomenon of band gaps; typically, domains of energies or frequencies in
which wave propagation is forbidden. In what follows, the topics of
electronic [28] and photonic bandgaps [51, 142], are addressed.

3.2.1 Electronic Band-Gap Crystals

3.2.1.1 Carbon Nanotubes

Carbon nanotubes (CNTs) were already introduced in Chapter 1. They are
a relatively new type of material and are considered by many to be the