Quantitative examination of the collapse of spin splitting in the quantum Hall regime

We have quantitatively tested the theoretical model on the collapse of spin slitting in the quantum Hall effect regime proposed by Fogler and Shklovskii [Phys. Rev. B 52, 17366 (1995)] in a high-mobility two-dimensional electron system (2DES) realized in a heterojunction insulated-gate field-effect transistor. In the 2DES density range between n $=$ 2 ×{} 10¹⁰ and 2 ×{} 10¹¹ cm^-2, the Landau level number N displays a power-law dependence on the critical electron density nc where the spin splitting collapses and N $=$ 11.47 ×{} nc{}^{0.64±{}0.01}$ (${n}c$ is in units of 10${}¹¹$ cm${}^{{-}2}$). This power-law dependence is in good agreement with the theoretical prediction in the low-density regime.