Inversion-layer width, electron-electron interactions, and the fractional quantum Hall effect

The current understanding of the fractional quantum Hall effect is based on the incompressible quantum fluid state proposed by Laughlin [Phys. Rev. Lett. 50, 1395 (1983)]. For a two-dimensional electron gas with Coulombic electron-electron interactions this proposal has been justified by demonstrating that Laughlin's state is lower in energy than the charge-density-wave state of the same system. In an actual inversion layer, the effective electron-electron interaction is strongly modified when the electron-electron separation becomes comparable with the inversion layer width. In this Rapid Communication we demonstrate that this modification results in a substantial reduction in the energy of both Laughlin and charge-density-wave states, but nevertheless leaves Laughlin's state lower in energy.