The diverse applications of terahertz (THz) radiation and its importance to fundamental science makes finding ways to generate, manipulate and detect THz 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 THz science and technology. This article describes the past, current, and future of THz science and technology of carbon nanotubes and graphene. We will review fundamental studies such as THz dynamic conductivity, THz nonlinearities and ultrafast carrier dynamics as well as THz applications such as THz sources, detectors, modulators, antennas and polarizers.

We present exact analytical solutions for the zero-energy modes of two-dimensional massless Dirac fermions fully confined within a smooth one-dimensional potential $V\left(x\right)=-\alpha /\text{cosh}\left(\beta x\right)$, 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 $\alpha /\beta$ 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.

The bound-state energy eigenvalues for the two-dimensional Kepler problem are found to be degenerate. This “accidental” degeneracy is due to the existence of a two-dimensional analog of the quantum-mechanical Runge–Lenz vector. Reformulating the problem in momentum space leads to an integral form of the Schrödinger equation. This equation is solved by projecting the two-dimensional momentum space onto the surface of a three-dimensional sphere. The eigenfunctions are then expanded in terms of spherical harmonics, and this leads to an integral relation in terms of special functions which has not previously been tabulated. The dynamical symmetry of the problem is also considered, and it is shown that the two components of the Runge–Lenz vector in real space correspond to the generators of infinitesimal rotations about the respective coordinate axes in momentum space.

We present exact analytical zero-energy solutions for a class of smooth-decaying potentials, showing that the full confinement of charge carriers in electrostatic potentials in graphene quantum dots and rings is indeed possible without recourse to magnetic fields. These exact solutions allow us to draw conclusions on the general requirements for the potential to support fully confined states, including a critical value of the potential strength and spatial extent.