Ballistic conduction in single-walled carbon nanotubes

Single-walled carbon nanotubes have the ability to conduct electricity. This conduction can be ballistic, diffusive, or based on scattering. When ballistic in nature conductance can be treated as if the electrons experience no scattering. Single-walled carbon nanotubes have the ability to conduct electricity. This conduction can be ballistic, diffusive, or based on scattering. When ballistic in nature conductance can be treated as if the electrons experience no scattering. Conduction in single-walled carbon nanotubes is quantized due to their one-dimensionality and the number of allowed electronic states is limited, if compared to bulk graphite. The nanotubes behave consequently as quantum wires and charge carriers are transmitted through discrete conduction channels. This conduction mechanism can be either ballistic or diffusive in nature, or based on tunneling. When ballistically conducted, the electrons travel through the nanotubes channel without experiencing scattering due to impurities, local defects or lattice vibrations. As a result, the electrons encounter no resistance and no energy dissipation occurs in the conduction channel.In order to estimate the current in the carbon nanotube channel, the Landauer formula can be applied, which considers a one-dimensional channel, connected to two contacts – source and drain. Assuming no scattering and ideal (transparent) contacts, the conductance of the one-dimensional system is given by G = G0NT, where T is the probability that an electron will be transmitted along the channel, N is the number of the channels available for transport, and G0 is the conductance quantum 2e2/h = (12.9kΩ)−1. Perfect contacts, with reflection R = 0, and no back scattering along the channel result in transmission probability T = 1 and the conductance of the system becomes G = (2e2/h) N. Thus each channel contributes 2G0 to the total conductance.For metallic armchair nanotubes, there are two subbands, which cross the Fermi level, and for semiconducting nanotubes – bands which don’t cross the Fermi level. Thus there are two conducting channels and each band accommodates two electrons of opposite spin. Thus the value of the conductance is G = 2G0 = (6.45 kΩ)−1. In a non-ideal system, T in the Landauer formula is replaced by the sum of the transmission probabilities for each conduction channel. When the value of the conductance for the above example approaches the ideal value of 2G0, the conduction along the channel is said to be ballistic. This happens when the scattering length in the nanotube is much greater than the distance between the contacts.If a carbon nanotube is a ballistic conductor, but the contacts are nontransparent, the transmission probability, T, is reduced by back-scattering in the contacts. If the contacts are perfect, the reduced T is due to back-scattering along the nanotube only.When the resistance measured at the contacts is high, one can infer the presence of Coulomb blockade and Luttinger liquid behavior for different temperatures. Low contact resistance is a prerequisite for investigating conduction phenomena in CNTs in the high transmission regime. When the size of the CNT device scales with the electron coherence length, important in the ballistic conduction regime in CNTs becomes the interference pattern arising when measuring the differential conductance d I / d V {displaystyle dI/dV} as a function of the gate voltage. This pattern is due to the quantum interference of multiply reflected electrons in the CNT channel. Effectively, this corresponds to a Fabry-Perot resonator, where the nanotube acts as a coherent waveguide and the resonant cavity is formed between the two CNT-electrode interfaces. Phase coherent transport, electron interference, and localized states have been observed in the form of fluctuations in the conductance as a function of the Fermi energy.