Stationary scattering solution and logic operations in X-coupled tight-binding chains

The realization of logical operations on X-shaped structures consisting of two discrete input chains, which are linearly connected to two output chains through a central coupling region, is investigated. We provide the exact stationary scattering solution for the harmonic waves propagating in the proposed structure and report the full transmission spectrum. We show that a number of Boolean logic operations can be implemented using a digitization scheme of the output signal based on the amplitude modulation of the transmission coefficients. In particular, we show that the relative phase between input harmonics can be used as a control parameter to select the desired logic operation. A detailed study of the contrast ratio is used to identify optimal regions in the parameter space for the operation of each logical function. (c) 2022 Elsevier B.V. All rights reserved.

Automated summary

This study investigates the realization of logical operations on X-shaped structures consisting of two discrete input chains connected to two output chains. The stationary scattering solution and the transmission spectrum of harmonic waves in the proposed structure are provided. It is shown that various Boolean logic operations can be implemented by digitizing the output signal using amplitude modulation. The relative phase between input harmonics can be used as a control parameter, and optimal regions in the parameter space for each logical function are identified through a detailed study of the contrast ratio.