Holes and Hall Effect

The concept of hole, a quasiparticle with a charge +e, greatly simplifies the explanation of positive Hall coefficient R_H. Due to the Lorentz force, if the charge carrier is hole/electron, then the R_H is positive/negative. Several textbooks have given rigorous and excellent explanations about the property of the holes. However, some are puzzled by this question: the current is formed by the flow of the electrons regardless we say the carrier is hole or electron; and the holes are just the vacant orbitals in an energy band, which is not a real particle. Therefore, the Lorentz force direction should be always the same and R_H should be always negative. Here we use plain language to answer this question. We emphasize that free electron model is invalid; quantum effect and interaction between an electron and crystal lattice must be considered.