Consideration of quantum-dimensional effects in designing plasmon-acoustic devices of the terahertz frequency range

Background. Graphene and boron nitride nanoribbons of hexagonal syngony are promising materials for use in nanoacoustics and nanoplasmonics as transmission lines of the terahertz frequency range. Meanwhile, their nanoscale width leads to a number of quantum-dimensional effects. There are resistances, inductances and capacitances per unit length which cannot be ignored even in the ballistic regime of the free charges transport. The aim of the study is to show the significant influence of these values on the electrical and wave parameters of such devises. Materials and methods. The objects of the study were nanoribbons made of graphene (Gr) and 2D hexagonal boron nitride (h-BN) isomorphic to it. The work used well-known analytical methods of classical microwave electronics, quantum physics and the band theory of the solid state physics in relation to nanoscale 2D crystal structures. Results. Expressions are obtained for the values of the quantum resistance, inductance, and capacitance per unit length of an electrically conductive nanoribbon of limited width depending on the corresponding quanta and the number of channels of electrical conductivity due to the width of the nanoribbon, the Fermi wave number for the free carriers, spin and valley degeneracy of their energy states. It is shown that the quantum inductance and capacitance of a nanoribbon at terahertz frequencies can exceed by two orders of magnitude the corresponding characteristics of the same nanoribbon for surface plasmon polaritons. The results are illustrated by the example of a plasmon-acoustic transducer of the terahertz frequency range on the graphene-hexagonal boron nitride structure. Conclusions. The quantum inductance and capacitance per unit length of graphene nanoribbon at terahertz frequencies can exceed their corresponding values for surface plasmon polaritons in the same nanoribbon by two orders of magnitude. This result taking into account quantum-dimensional effects when designing nanoelectromechanical devises.