R. R. Hartmann — Page 2

arXiv2011

Excitons in narrow-gap carbon nanotubes

We calculate the exciton binding energy in single-walled carbon nanotubes with narrow band gaps, accounting for the quasi-relativistic dispersion of electrons and holes. Exact analytical solutions of the quantum relativistic two-body problem are obtain 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 quasi-metallic nanotubes and that their THz applications are feasible.

cond-mat.mes-hall↗

arXiv2010

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)= - α/cosh(βx), 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 α/β for which the first mode appears, in striking contrast to the non-relativistic 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.

cond-mat.mes-hall↗