Spin-Peierls effect in spin-polarization of fractional quantum Hall states

Electron spin-polarizations have been measured in the fractional quantum Hall effect. In experimental curves, a number of plateaus appear, some that are wide and others that are narrow. In this paper, theoretical calculations are presented to explain these observations. In the Landau gauge, single electron orbitals have the shape of equally spaced parallel lines. When a specific electron configuration of these orbitals is considered, the minimum classical Coulomb energy is obtained. Residual Coulomb interactions produce spin exchange interactions. If the spin-Peierls effect (modulation of the intervals between orbitals) is also taken into consideration, a new small energy gap appears. The total energy resulting from this modulation is smaller than the total energy in the non-modulated case, indicating that the modulation actually occurs. Eigenenergies are calculated under this modulation. The calculated spin-polarization curves then exhibit both narrow and wide plateaus, and are in good agreement with the experimental data.