A technique to directly excite Luttinger liquid collective modes in carbon nanotubes at GHz frequencies

We present a technique to directly excite Luttinger liquid collective modes in carbon nanotubes at GHz 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 2d plasmons and should work well for 1d plasmons. Tubes of length 100 microns must be grown for GHz resonance frequencies. Ohmic contact is not necessary with our technique; capacitive contacts can work.