Page 124 - Principles and Applications of NanoMEMS Physics

112 Chapter 3

L h
Z , c DM = K = , (87)
C Q 2 e 2

which Burke interprets as defining the ratio of excitation voltage to elicited
current when the spin wave is excited.
With diameters of the order of approximately 1nm, CNTs are ideal
systems where the characteristics of Lüttinger liquids, namely, strong
electron-electron interaction and spin-charge separation, should be manifest.
Accordingly, efforts have been expended to develop ways of characterizing
and ascertaining such behavior. Noticeable among these, is experimental
work by Bockrath et al. [149] who deduced, from the measured 3D-1D
α
tunneling conductance dI dV ∝V , CNT Lüttinger parameters g with
values between 0.2 and 0.3. These were extracted from comparison of
measurement to the theoretical relations α = (g − 1 − 1 ) 4/ or
End
α = (g − 1 + g − 2 ) 8/ , for 3D-1D contacts located at the end or at the
Bulk
bulk, respectively, of the CNT [151], see Fig. 3-19.

Bulk Contact
Bulk Contact

End Contact
End Contact
e e - -
e e - -
Luttinger Liquid
L>>L E E Luttinger Liquid
L>>L
Figure 3-19. 3D-1D contact to carbon nanotube. (After [151].)

Similarly, efforts have been expended, and are being vigorously pursued,
to uncover the predicted spin-charge separation. These include proposals to
directly excite Lüttinger liquid behavior in CNTs by impressing microwave
voltage waves in CNTs acting as transmission lines [149].

3.2.1.2 Superconductors

The phenomenon of superconductivity manifests itself as the drop in the
electrical resistance of metals and alloys at sufficiently low temperatures,
accompanied by the inhibition of magnetic fields from penetrating inside of
them [28]. Conversely, a material in the superconducting state loses this
property when its temperature is raised past a critical temperature, T , or it
c