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.