Electrical Conduction in Graphene and Nanotubes by Shigeji Fujita and Akria Suzuki
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Electrical Conduction in Graphene and Nanotubes by Shigeji Fujita and Akria Suzuki


Brilliant diamond and carbon black (graphite) are both made of carbon (C). Diamond is an insulator while graphite is a good conductor. This difference arises from the lattice structure. Graphite is a layered material made up of sheets, each forming a two-dimensional (2D) honeycomb lattice, called graphene. The electrical conduction mainly occurs through graphene sheets. Carbon nanotubes were discovered by Iijima1) in 1991. The nanotubes ranged from 4 to 30 nm in diameter and were microns (μm) in length, had scroll-type structures, and were called Multi-walled Nanotubes (MWNTs) in the literature. Single-Wall Nanotubes (SWNTs) have a size of about 1 nm in diameter and microns in length.

This is a simple two-dimensional material. It is theorists’ favorite system. The electrical transport properties along the tube present, however, many puzzles, as is explained below. Carbon nanotubes are very strong and light. In fact, carbon fibers are used to make tennis rackets. Today’s semiconductor technology is based on silicon (Si) devices. It is said that carbon chips, which are stronger and lighter, may take the place of silicon chips in the future. It is, then, very important to understand the electrical transport properties of carbon nanotubes. The present book has as its principal topics electrical transport in graphene and carbon nanotubes. The conductivity σ in individual carbon nanotubes varies, depending on the tube radius and the pitch of the sample.

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In many cases the resistance decreases with increasing temperature while the resistance increases in the normal metal. Electrical conduction in SWNTs is either semiconducting or metallic, depending on whether each pitch of the helical line connecting the nearest-neighbor C-hexagon centers contains an integral number of hexagons or not. The second alternative occurs more often since the pitch is not controlled in the fabrication process. The room-temperature conductivity in metallic SWNTs is higher by two or more orders of magnitude than in semiconducting SWNTs. Currents in metallic SWNTs do not obey Ohm’s law linearity between current and voltage. Scanned probe microscopy shows that the voltage does not drop along the tube length, implying a superconducting state.

The prevailing theory states that electrons run through the one-dimensional (1D) tube ballistically. But this interpretation is not the complete story. The reason why the ballistic electrons are not scattered by impurities and phonons is unexplained. We present a new interpretation in terms of the model in which superconducting Bose-condensed Cooper pairs (bosons) run as a supercurrent. In our text we start with the honeycomb lattice, construct the Fermi surface, and develop Bloch electron dynamics based on the rectangular unit cell model. We then use kinetic theory to treat the normal electrical transport with the assumption of “electrons,” “holes,” and Cooper pairs as carriers.

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