We show that thermal rectification (TR) in asymmetric graphene nanoribbons (GNRs) is originated from phonon confinement in the lateral dimension, which is a fundamentally new mechanism different from that in macroscopic heterojunctions. Our molecular dynamics simulations reveal that, though TR is significant in nanosized asymmetric GNRs, it diminishes at larger width. By solving the heat diffusion equation, we prove that TR is indeed absent in both the total heat transfer rate and local heat flux for bulk-size asymmetric single materials, regardless of the device geometry or the anisotropy of the thermal conductivity. For a deeper understanding of why lateral confinement is needed, we have performed phonon spectra analysis and shown that phonon lateral confinement can enable three possible mechanisms for TR: phonon spectra overlap, inseparable dependence of thermal conductivity on temperature and space, and phonon edge localization, which are essentially related to each other in a complicated manner. Under such guidance, we demonstrate that other asymmetric nanostructures, such as asymmetric nanowires, thin films, and quantum dots, of a single material are potentially high-performance thermal rectifiers. KEYWORDS: Thermal rectification, phonon lateral confinement, phonon localization, edge/surface effect, molecular dynamics, phonon spectra I nspired by the impact of electric diodes on the electronics industry, extensive attention has been given to the search of rectification of various other transport processes.1−3 Thermal rectification (TR) is a diode-like behavior where the heat current changes in magnitude when the applied temperature (T) bias is reversed in direction. A perfect thermal rectifier would be one that is highly thermal conductive in one direction while insulating in the other, and it is expected to work as a promising thermal management component of electronics as chip size continues decreasing or as a stand-alone thermally driven computing system replacing the electronic ones in certain conditions.Numerous studies have predicted or demonstrated the existence of TR in bulk or nanosized systems, most of which are heterojunctions (HJ) or graded systems.3−11 For twosegment systems, TR was usually attributed to the different Tdependence of the thermal conductivity (κ), 5,7 and for interfaces TR has been interpreted as the different phonon spectra mismatch before and after reversing the applied T bias. Phonon localization was suggested to play a role as well. 12,13 Recently, TR was also predicted to occur in asymmetric pristine carbon nanostructures, 13−17 which are composed of a single material and are attractive for their simple structure and high thermal conductance. 18 However, the origin of TR in such homogeneous nanostructures remains unclear. In this work, we have observed, using molecular dynamics and analytical derivations, that phonon confinement in the lateral dimension is required for TR to occur in asymmetric homogeneous structures made of a single material. We further show that...