New insight into the Hall effect

In this paper, we develop a unified theory for describing Hall effect in various electronic systems based on a pure electron picture (without the hole concept). We argue that the Hall effect is the magnetic field induced symmetry breaking of the charge carrier's spatial distribution. Due to the interaction of the charge carriers and the ion lattice, there are two possible symmetry breaking mechanisms which cause different signs of Hall coefficient in a Hall material. The scenario provides an explicit explanation of the sign different of the Hall coefficient in the N-type and P-type semiconductors, the sign reversal induced by both temperature and magnetic field in different materials, and the integer and fractional quantum Hall effect (QHE) in two-dimensional electron gas (2DEG) of GaAs/AlGaN heterostructures.