Influence of Two-Dimensional Angular Momentum on Statistical Properties with Application to the Quantum Hall Effect

This work proposes that, in a two-dimensional electron gas, the angular momentum of electrons in Landau levels introduces an additional geometric phase upon the exchange of identical particles. 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 filling factors, 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 conventional Landau levels. The quantum Hall plateau originates from the locking of the condensate carrier density at the corresponding filling factor: additionally injected electrons, which do not satisfy the condensation condition and therefore lack superfluid character, do not contribute to conduction, thus maintaining a constant Hall conductance. The theory naturally accounts for the chiral nature of the longitudinal current and its boundary localization. Based on this framework, this work provides a unified perspective on the integer quantum Hall effect and the fractional quantum Hall effect (encompassing both odd- and even-denominator cases), fermionic and bosonic systems, as well as two- and three-dimensional situations.