Kinematically restricted phonon transmission in partly-unzipped tubes of square and triangular lattices

TL;DR

This paper analyzes how scalar phonons transmit through partly unzipped square and triangular lattice tubes, providing exact formulas for reflectance, transmittance, and ballistic conductance based on Chebyshev polynomials.

Contribution

It introduces an exact analytical method for calculating phonon transmission in unzipped lattice tubes, considering out-of-plane and radial phonons with explicit formulas.

Findings

Exact expressions for reflectance and transmittance derived

Ballistic conductance formulas provided

Transmission characteristics depend on lattice geometry

Abstract

An analysis of the transmission of `scalar' phonons across partially unzipped square and triangular lattice tubes, assuming nearest neighbor interactions between particles, is presented. The phonon transport is assumed to involve the out-of-plane phonons in the unzipped portion and the radial phonons in the tubular portion. An exact expression of reflectance and transmittance for the waves incident from either portions of the waveguide are provided explicitly, in terms of the Chebyshev polynomials, which leads to the provision of a simple expression for the ballistic conductance.