Alternative Interpretation and Prediction of Quantum Hall Effect via Electron Pairing Picture

Abstract

As a two-body system, hydrogen atom with quantum exact solution played an important role for explaining shell structure of multi-electron atoms. Inspired by this, we suggest an alternative interpretation of the integer and fractional quantum Hall effect (QHE) by establishing a direct connection between the exact solutions of a two-dimensional (2D) magnetically trapped electron-pair and the “fundamental” (non-fine) Hall hierarchies of a multi-electron system. We analyze the topology of the exact pair states and report the filling factors of the lowest Landau level based on the exact solutions, which fit the previously and recently reported spectrum of experimental data on the QHE states well and predict some new Hall plateaus for the plateau positions and the eigenenergies reflecting stability and plateau widths. The theoretical prediction associated with the relatively lower minima of the diagonal resistivity is in accurate agreement with the experimental datum spectrum of the fundamental QHE hierarchies.