We present exact analytical solutions for the zero-energy modes of two-dimensional massless Dirac fermions fully confined within a smooth one-dimensional potential V͑x͒ =−␣ / cosh͑␤x͒, which provides a good fit for potential profiles of existing top-gated graphene structures. We show that there is a threshold value of the characteristic potential strength ␣ / ␤ for which the first mode appears, in striking contrast to the nonrelativistic case. A simple relationship between the characteristic strength and the number of modes within the potential is found. An experimental setup is proposed for the observation of these modes. The proposed geometry could be utilized in future graphene-based devices with high on/off current ratios.

Abstract. The diverse applications of terahertz radiation and its importance to fundamental science makes finding ways to generate, manipulate, and detect terahertz radiation one of the key areas of modern applied physics. One approach is to utilize carbon nanomaterials, in particular, single-wall carbon nanotubes and graphene. Their novel optical and electronic properties offer much promise to the field of terahertz science and technology. This article describes the past, current, and future of the terahertz science and technology of carbon nanotubes and graphene. We will review fundamental studies such as terahertz dynamic conductivity, terahertz nonlinearities, and ultrafast carrier dynamics as well as terahertz applications such as terahertz sources, detectors, modulators, antennas, and polarizers.

We predict a double-resonant feature in the magnetic field dependence of the phonon-mediated longitudinal conductivity xx of a two-subband quasi-two-dimensional electron system in a quantizing magnetic field. The two sharp peaks in xx appear when the energy separation between two Landau levels belonging to different size-quantization subbands is favorable for acoustic-phonon transitions. One-phonon and two-phonon mechanisms of electron conductivity are calculated and compared. The phonon-mediated interaction between the intersecting Landau levels is considered and no avoided crossing is found at thermal equilibrium.