Mesoscopic Phonon Transmission through a Nanowire-Bulk Contact

TL;DR

This paper calculates how low-frequency acoustic phonons transmit through a nanowire-bulk contact, revealing that transmission diminishes with the square of frequency and thermal conductance drops cubically with temperature.

Contribution

It introduces a perturbative method to analyze mesoscopic phonon transmission at low frequencies using elasticity theory and boundary conditions.

Findings

Transmission probability vanishes as frequency squared at low frequencies.

Transport is dominated by the longitudinal channel, acting as a monopole source.

Thermal conductance decreases with the cube of temperature.

Abstract

We calculate the frequency-dependent mesoscopic acoustic phonon transmission probability through the abrupt junction between a semi-infinite, one-dimensional cylindrical quantum wire and a three-dimensional bulk insulator, using a perturbative technique that is valid at low frequency. The system is described using elasticity theory, and traction-free boundary conditions are applied to all free surfaces. In the low-frequency limit the transmission probability vanishes as the frequency squared, the transport being dominated by the longitudinal channel, which produces a monopole source of elastic radiation at the surface of the bulk solid. The thermal conductance between an equilibrated wire nonadiabatically coupled to a bulk insulator should therefore vanish with temperature at temperature cubed.