Nonequilibrium Green’s functions (NEGF) in vibrational energy transport: a topical review

ABSTRACT Recent advances in fabrication techniques have enabled the development of materials sculpted at the nanoscale (~10 nm). These “nano-materials” could revolutionize thermal management technologies by providing novel ways to manipulate energy propagation in solids. Atomistic simulations are critical to forging this revolution, given their ability to describe a system’s dynamics on an atom by atom basis. This topical review focuses on nonequilibrium Green’s functions (NEGF) simulations to model vibrational energy propagation at the nanoscale. NEGF is an atomistic and purely quantum mechanical approach well-suited to compute thermal transport in spatially varying systems such as “nano-materials.” This review presents the NEGF methodology from a top-to-bottom perspective, focusing on the concepts behind the mathematical expressions. We start describing the implementation of NEGF that assumes harmonic interatomic potentials (h-NEGF) and some recent advances that distinguish the transport contributions by different polarizations. This review also discusses the less common implementation of NEGF that includes the anharmonic terms of the potentials (a-NEGF), outlining existing approximations and standing challenges. Our success in tackling these challenges will determine whether we will harness the full potential of NEGF to describe thermal transport from a quantum mechanical standpoint.