Abstract
This work proposes that, in a two-dimensional electron gas, the angular momentum of electrons in Landau levels induces an additional geometric phase upon identical particle exchange. This phase couples with the intrinsic exchange phase associated with spin, thereby modifying the effective quantum statistics of electrons. As a result, at integer or certain fractional fillings, spatially adjacent electrons effectively obey Bose statistics and form composite bosons, which subsequently undergo Bose–Einstein condensation. A finite energy gap opens between the condensed electrons and those occupying the normal Landau levels. The quantum Hall plateau arises from the locking of the condensate carrier density at the corresponding filling factor: additional injected electrons, which do not satisfy the condensation condition, behave as quasiparticles in the normal Landau levels and do not contribute to conduction, thus preserving a constant Hall conductance. The theory naturally yields the chiral nature of the longitudinal current and its boundary localization. Based on this framework, this work offers a unified perspective on the integer quantum Hall effect and fractional quantum Hall effects, including those with odd and even denominators.
