Takeshi Nakanishi

We demonstrate logic circuits with field-effect transistors based on single carbon nanotubes. Our device layout features local gates that provide excellent capacitive coupling between the gate and nanotube, enabling strong electrostatic doping of the nanotube from p-doping to n-doping and the study of the nonconventional long-range screening of charge along the one-dimensional nanotubes. The transistors show favorable device characteristics such as high gain (>10), a large on-off ratio (>10(5)), and room-temperature operation. Importantly, the local-gate layout allows for integration of multiple devices on a single chip. Indeed, we demonstrate one-, two-, and three-transistor circuits that exhibit a range of digital logic operations, such as an inverter, a logic NOR, a static random-access memory cell, and an ac ring oscillator.

The absence of back scattering in carbon nanotubes is shown to be ascribed to Berry's phase which corresponds to a sign change of the wave function under a spin rotation of a neutrino-like particle in a two-dimensional graphite. Effects of trigonal warping of the bands appearing in a higher order k · p approximation are shown to give rise to a small probability of back scattering.

The effective potential of an impurity in a k · p scheme is derived in two-dimensional graphite sheet. When the potential range is smaller than the lattice constant, it has an off-diagonal matrix element between K and K ′ points comparable to the diagonal element. With the increase of the range, this off-diagonal element decreases rapidly and the diagonal element for envelopes at A and B sites becomes identical. The crossover between these two regimes occurs around the range smaller than the lattice constant. In the latter regime, back scattering between states with + k and - k vanishes identically for the bands crossing the Fermi level in the absence of a magnetic field, leading to an extremely large conductivity. The absence of the back scattering disappears in magnetic fields, giving rise to a huge positive magnetoresistance.

Graphene is a one-atom-thick layer of graphite, where low-energy electronic states are described by the massless Dirac fermion. The orientation of the graphene edge determines the energy spectrum of π-electrons. For example, zigzag edges possess localized edge states with energies close to the Fermi level. In this review, we investigate nanoscale effects on the physical properties of graphene nanoribbons and clarify the role of edge boundaries. We also provide analytical solutions for electronic dispersion and the corresponding wavefunction in graphene nanoribbons with their detailed derivation using wave mechanics based on the tight-binding model. The energy band structures of armchair nanoribbons can be obtained by making the transverse wavenumber discrete, in accordance with the edge boundary condition, as in the case of carbon nanotubes. However, zigzag nanoribbons are not analogous to carbon nanotubes, because in zigzag nanoribbons the transverse wavenumber depends not only on the ribbon width but also on the longitudinal wavenumber. The quantization rule of electronic conductance as well as the magnetic instability of edge states due to the electron-electron interaction are briefly discussed.