Mechanics of graphene in context

Mechanics of graphene in context Junjie Chen Department of Energy and Power Engineering, School of Mechanical and Power Engineering, Henan Polytechnic University, 2000 Century Avenue, Jiaozuo, Henan, 454000, P.R. China Contributor: Junjie Chen, ORCID: 0000-0002-5022-6863, E-mail address: koncjj@gmail.com Graphene is a two-dimensional form of crystalline carbon, either a single layer of carbon atoms forming a honeycomb lattice or several coupled layers of this honeycomb structure. The word graphene, when used without specifying the form, usually refers to single-layer graphene. Graphene is a parent form of all graphitic structures of carbon: graphite, which is a three-dimensional crystal consisting of relatively weakly coupled graphene layers; nanotubes, which may be represented as scrolls of graphene; and buckyballs, spherical molecules made from graphene with some hexagonal rings replaced by pentagonal rings. The basic electronic structure of graphene and, as a consequence, its electric properties are very peculiar. By applying a gate voltage or using chemical doping by adsorbed atoms and molecules, one can create either electron or hole conductivity in graphene that is similar to the conductivity created in semiconductors. However, in most semiconductors there are certain energy levels where electrons and holes do not have allowed quantum states, and, because electrons and holes cannot occupy these levels, for certain gate voltages and types of chemical doping, the semiconductor acts as an insulator. Graphene, on the other hand, does not have an insulator state, and conductivity remains finite at any doping, including zero doping. Existence of this minimal conductivity for the undoped case is a striking difference between graphene and conventional semiconductors. Electron and hole states in graphene relevant for charge-carrier transport are similar to the states of ultra-relativistic quantum particles, that is, quantum particles moving at the speed of light. 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. Graphene provides a bridge between materials science and some areas of fundamental physics, such as relativistic quantum mechanics. There is another reason why graphene is of special interest to fundamental science: it 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 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 or by chemical modification of 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.Contributor: Junjie Chen, ORCID: 0000-0002-5022-6863, E-mail address: koncjj@gmail.com, Department of Energy and Power Engineering, School of Mechanical and Power Engineering, Henan Polytechnic University, 2000 Century Avenue, Jiaozuo, Henan, 454000, P.R. Chin