Independent Channel Method for Lattice Thermal Conductance in Corrugated Graphene Ribbons

Graphene's extraordinary thermal conductivity makes it a compelling material for heat management in microelectronic circuits, lithium-ion batteries, and thermoelectric devices. In this article, we investigate its vibrational modes using a Born-von Karman model that includes first- and second-nearest-neighbor interactions. The resulting phonon dispersion relations agree well with experimental data, including acoustic flexural modes. To analyze phonon transport in mesoscopic graphene ribbons, we use both the Kubo-Greenwood and Landauer formalisms, as well as an independent channel method, which analytically maps zigzag-edged hexagonal ribbons into a set of single and dual chains via a unitary transformation. The resulting lattice thermal conductance spectra exhibit quantized steps that are smoothed in the presence of corrugations. We further explore the effects of temperature-induced rippling and buckling disorders on the phonon transport in graphene ribbons suspended over trenches. The predicted thermal conductance as a function of length and temperature closely matches experimental measurements, demonstrating the effectiveness of the independent channel method for the fully real-space modeling of corrugated graphene ribbons.