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Porous graphene and graphite are increasingly utilized in electrochemical energy storage and solar-thermal applications due to their unique structural and thermal properties. In this study, we conduct a comprehensive analysis of the lattice thermal transport and spectral phonon characteristics of holey graphite and multilayer graphene. Our results reveal that phonon modes propagating obliquely with respect to the graphene basal planes are the primary contributors to cross-plane thermal transport. These modes exhibit a predominantly ballistic nature, resulting in an almost linear increase in cross-plane thermal conductivity with the number of layers. The presence of nanoholes in graphene induces a broadband suppression of cross-plane phonon transport, whereas lithium-ion intercalation shows potential to enhance it. These findings provide critical insights into the mechanisms governing cross-plane heat conduction in key graphene-based structures, offering valuable guidance for thermal management and engineering of van der Waals materials. 

The Anderson localization of phonons in disordered superlattices has been proposed as a route to suppress thermal conductivity beyond the limits imposed by conventional scattering mechanisms. A commonly used signature of phonon localization is the emergence of the nonmonotonic dependence of thermal conductivity κ on system length L, i.e., a κ-L maximum. However, such behavior has rarely been observed. In this work, we conduct extensive non-equilibrium molecular dynamics (NEMD) simulations, using the LAMMPS package, on both periodic superlattices (SLs) and aperiodic random multilayers (RMLs) constructed from Si/Ge and Lennard-Jones materials. By systematically varying acoustic contrast, interatomic bond strength, and average layer thickness, we examine the interplay between coherent and incoherent phonon transport in these systems. Our two-phonon model decomposition reveals that coherent phonons alone consistently exhibit a strong nonmonotonic κ-L. This localization signature is often masked by the diffusive, monotonically increasing contribution from incoherent phonons. We further extract the ballistic-limit mean free paths for both phonon types, and demonstrate that incoherent transport often dominates, thereby concealing localization effects. Our findings highlight the importance of decoupling coherent and incoherent phonon contributions in both simulations and experiments. This work provides new insights and design principles for achieving phonon Anderson localization in superlattice structures. 

Superlattices are a distinctive class of artificial nanostructures formed by the periodic stacking of two or more materials. The high density of interfaces in these structures often gives rise to exotic physical properties. In the context of thermal transport, it is well established that such interfaces can significantly scatter particle-like phonons while also inducing constructive or destructive interference in wave-like phonons, depending on the relationship between the phonons’ coherence lengths and the superlattice’s period thickness. In this work, we systematically investigate the effect of temperature on the spectral energy density of phonon modes in superlattices. Additionally, we examine how variations in superlattice period thickness influence phonon lifetimes and energy density. Our findings provide critical insights into the spectral phonon properties of superlattices, particularly in terms of their coherence and lifetimes.