Charge carrier carriers by leaving behind holes (electrons) in the other band. In other words, charge carriers are particles/electrons that are free to move (carry the charge). They get charged at the battery/cell, and then flow throughout the circuit, giving energy to any components in the way, then when out of charge and towards the end of the circuit, they get re-charged by the battery/cell. Charge carrier In physics, a charge carrier is a particle or quasiparticle that is free to move, carrying an electric charge, especially the particles that carry electric charges in electrical conductors. Examples are electrons, ions and holes.
Particle in a ring in that case are identical to the energy eigenfunctions of the particle on a ring. The statement that any wavefunction for the particle on a ring can be written as a superposition of energy eigenfunctions is exactly identical to the Fourier theorem about the development of any periodic function in a Fourier series. This simple model can be used to find approximate energy levels of some ring molecules, such as benzene. In organic chemistry, aromatic compounds contain atomic rings, such as benzene rings (the Kekulé structure) consisting of five or six, usually carbon, atoms. So does the surface of "buckyballs"