Excitation gap in the fractional quantum Hall effect: Finite layer thickness corrections

Excitation energy for the = (1/3) fractional quantum Hall effect state is calculated by exact numerical diagonalization for a small number of electrons in the spherical geometry keeping the finite width of the quasi-two-dimensional layer in the calculation. It is found that for actual experimental systems finite layer thickness corrections reduce the excitation gap by as much as a factor of two, bringing experiment and theory much closer together. Calculated thickness effect also qualitatively explains the experimentally observed saturation in the activation energy at the highest magnetic fields.