Luttinger liquid theory as a model of the gigahertz electrical properties of carbon nanotubes

We present a technique to directly excite Luttinger liquid collective modes in carbon nanotubes at gigahertz frequencies. By modeling the nanotube as a nano-transmission line with distributed kinetic and magnetic inductance as well as distributed quantum and electrostatic capacitance, we calculate the complex frequency-dependent impedance for a variety of measurement geometries. Exciting voltage waves on the nano-transmission line is equivalent to directly exciting the yet-to-be observed one-dimensional plasmons, the low energy excitation of a Luttinger liquid. Our technique has already been applied to two-dimensional plasmons and should work well for one-dimensional plasmons. Tubes of length 100 microns must be grown for gigahertz resonance frequencies. Ohmic contact is not necessary with our technique; capacitive contacts can work. Our modeling has applications in potentially Terahertz nanotube transistors and RF nanospintronics.