2. Methods
The honeycomb lattice of graphene actually consists of two sublattices, designated A and B, such that each atom in sublattice A is surrounded by three atoms of sublattice B and vice versa. This simple geometrical arrangement leads to the appearance that the electrons and holes in graphene have an unusual degree of internal freedom, usually called pseudospin. In fact, making the analogy more complete, pseudospin mimics the spin, or internal angular momentum, of subatomic particles. Within this analogy, electrons and holes in graphene play the same role as particles and antiparticles in quantum electrodynamics. This makes graphene a test bed for high-energy physics: some quantum relativistic effects that are hardly reachable in experiments with subatomic particles using particle accelerators have clear analogs in the physics of electrons and holes in graphene, which can be measured and studied more easily because of their lower velocity. Thus, graphene provides a bridge between materials science and some areas of fundamental physics.
There is another reason why graphene is of special interest to fundamental science. Graphene is the first and simplest example of a two-dimensional crystal, that is, a solid material that contains just a single layer of atoms arranged in an ordered pattern. Two-dimensional systems are of huge interest not only for physics and chemistry but also for other natural sciences. In many respects, two-dimensional systems are fundamentally different from three-dimensional systems. In particular, due to very strong thermal fluctuations of atomic positions that remain correlated at large distances, long-range crystalline order cannot exist in two dimensions. Instead, only short-range order exists, and it does so only on some finite scale of characteristic length, a caveat that should be noted when graphene is called a two-dimensional crystal. For this reason, two-dimensional systems are inherently flexural, manifesting strong bending fluctuations, so that they cannot be flat and are always rippled or corrugated. Graphene, because of its relative simplicity, can be considered as a model system for studying two-dimensional physics and chemistry in general. Other two-dimensional crystals besides graphene can be derived by exfoliation from other multilayer crystals, for example, hexagonal boron nitride, molybdenum disulfide, or tungsten disulfide, or by chemical modification of graphene, for example, hydrogenated graphene, or fluorinated graphene. Modern electronics are basically two-dimensional in that they use mainly the surface of semiconducting materials. Therefore, graphene and other two-dimensional materials are considered very promising for many such applications. Using graphene, for example, it should be possible to make electronic devices that are much thinner than devices made of traditional materials. Graphene does not have an insulator state, and conductivity remains finite at any doping.
The thermal transport characteristics of graphene nanoribbons are studied using molecular dynamics simulations. A specific heat flux imposed through the graphene nanoribbon modeled in this study is depicted schematically in Figure 1 in a shape of rectangle. The graphene nanoribbon is monolayer and thus can be considered as a single layer of carbon atoms with each atom bound to three neighbors in a honeycomb structure. The substantially flat monolayer of carbon atoms is usually referred to as the basal plane of the graphene nanoribbon. The monolayer graphene nanoribbon includes an edge irregularity, such as a zig-zag configuration edge or an armchair-configuration edge. The transverse edges at both ends of the graphene nanoribbon are rough, whereas the longitudinal edges at both sides of the graphene nanoribbon are substantially smooth. It is worth noting that the direction of heat flow is perpendicular to the irregularly shaped edges of the graphene nanoribbon. The transverse edges at both ends of the nanostructured graphene nanoribbon are atomically-disordered in the form of roughness. This edge disorder can degrade the thermal, electronic, and structural properties of the nanostructured graphene nanoribbon, including its electron mobility and strength. The graphene nanoribbon has a generally square shape with the width approximately equal to the length. The graphene nanoribbon has a generally square shape with the width approximately equal to the length.