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....