Transmission of waves across atomic step discontinuities in discrete nanoribbon structures

TL;DR

This paper derives exact solutions for wave transmission across atomic step discontinuities in discrete nanoribbon structures, providing insights into energy flux transmission in lattice waveguides with various boundary conditions.

Contribution

It introduces an exact Wiener-Hopf based method to analyze wave scattering in discrete nanoribbons with multiple boundary configurations, advancing understanding of wave transmission at atomic steps.

Findings

Exact transmission coefficients for energy flux are obtained.

Numerical results illustrate conductance variations across configurations.

Multiple boundary condition configurations are analyzed in detail.

Abstract

Scalar wave propagation across a semi-infinite step or step-like discontinuity on any one boundary of the square lattice waveguides is considered within nearest-neighbour interaction approximation. An application of the Wiener-Hopf method does yield an exact solution of the discrete scattering problem, using which, as the main result of the paper, the transmission coefficients for energy flux are obtained. It is assumed that a wave mode is incident from either side of the step and the question addressed is what fraction of incident energy is transmitted across the atomic step discontinuity. A total of ten configurations are presented that arise due to various placements of discrete Dirichlet and Neumann boundary conditions on the waveguide. Numerical illustrations of a measure of conductance are provided.