Richard R. Hartmann

Terahertz science and technology of carbon nanomaterials

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.

Smooth electron waveguides in graphene

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(x)=-{alpha}/cosh({beta}x), 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.

Quasi-exact solution to the Dirac equation for the hyperbolic-secant potential

We analyze bound modes of two-dimensional massless Dirac fermions confined within a hyperbolic secant potential, which provides a good fit for potential profiles of existing top-gated graphene structures. We show that bound states of both positive and negative energies exist in the energy spectrum and that there is a threshold value of the characteristic potential strength for which the first mode appears. Analytical solutions are presented in several limited cases and supercriticality is discussed.

Excitons in narrow-gap carbon nanotubes

We calculate the exciton binding energy in single-walled carbon nanotubes with narrow band gaps, accounting for the quasirelativistic dispersion of electrons and holes. Exact analytical solutions of the quantum relativistic two-body problem are obtained for several limiting cases. We show that the binding energy scales with the band gap, and conclude on the basis of the data available for semiconductor nanotubes that there is no transition to an excitonic insulator in quasimetallic nanotubes and that their THz applications are feasible.

Bound states in a hyperbolic asymmetric double-well

We report a new class of hyperbolic asymmetric double-well whose bound state wavefunctions can be expressed in terms of confluent Heun functions. An analytic procedure is used to obtain the energy eigenvalues and the criterion for the potential to support bound states is discussed.

Two-dimensional Dirac particles in a Pöschl-Teller waveguide

We obtain exact solutions to the two-dimensional (2D) Dirac equation for the one-dimensional Pöschl-Teller potential which contains an asymmetry term. The eigenfunctions are expressed in terms of Heun confluent functions, while the eigenvalues are determined via the solutions of a simple transcendental equation. For the symmetric case, the eigenfunctions of the supercritical states are expressed as spheroidal wave functions, and approximate analytical expressions are obtained for the corresponding eigenvalues. A universal condition for any square integrable symmetric potential is obtained for the minimum strength of the potential required to hold a bound state of zero energy. Applications for smooth electron waveguides in 2D Dirac-Weyl systems are discussed.

Terahertz transitions in quasi-metallic carbon nanotubes

We study interbanddipole transitions across curvature-induced narrow gaps in quasi-metallic single-walled carbon nanotubes. The curvature effects not only open a gap in the nanotube energy spectrum but also allow optical transitions, which happen to be in the highly- desired terahertz frequency range. Applying a magnetic field along the nanotube axis allows one to tune the frequency peaks in the spectral density of absorption.

Exciton states in narrow-gap carbon nanotubes

Quasi-exact solutions to the quantum relativistic two-body problem are obtained for a one-dimensional Woods-Saxon-like potential. The quantised positive energy spectrum is obtained in the square well potential limit in terms of a set of simple transcendental equations. This potential is used to calculate excitonic states in narrow-gap single-walled carbon nanotubes and the binding energy is shown to scale with the band gap.

Terahertz Applications of Carbon Nanotubes and Graphene Nanoribbons

The results of the theoretical study of interband THz transitions in narrow-gap carbon nanotubes and graphene nanoribbons are reported. We consider dipole transitions across magnetically-induced gaps in armchair nanotubes, curvature-induced gaps in quasi-metallic nanotubes and edge-effect induced gaps in armchair nanoribbons. A giant enhancement of the transition matrix elements is discovered for all three types of nanostructures.

Pair states in one-dimensional Dirac systems

This work was supported by the EU H2020 RISE Project CoExAN (Grant No. H2020-644076), and EU FP7 ITN NOTEDEV (Grant No. FP7-607521), FP7 IRSES Projects CANTOR (Grant No. FP7-612285), QOCaN (Grant No. FP7-316432), and InterNoM (Grant No. FP7-612624). R.R.H. acknowledges financial support from URCO (Project No. 09 F U 1TAY15-1TAY16) and Research Links Travel Grant by the British Council Newton Fund (Project No. 172695634).