  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.
