Distribution of electron density and magnetocapacitance in the regime of the fractional quantum Hall effect

This study investigates the distribution of electron density and magnetocapacitance in a two-dimensional electron liquid (TDEL) under a smooth random potential, specifically focusing on the fractional quantum Hall effect. The objective is to provide an analytical theory for nonlinear screening when the fractional gap is significantly smaller than the unscreened random potential. We utilized a narrow-gap approximation (NGA) to calculate key parameters including the electron density distribution function, the fraction of TDEL in the incompressible state, and the thermodynamic density of states. Additionally, the magnetocapacitance is computed to align with recent experimental data. Results indicated that the NGA lacked sufficient accuracy for comprehensive description, leading us to employ computer modeling for scenarios involving larger fractional gaps. Our findings also incorporated the interaction between anyons in the vicinity of fractional singularities to achieve a better fit to experimental observations. This comprehensive approach reveals critical insights into the behaviors of TDELs and emphasizes the importance of accounting for varying factors in magnetocapacitance studies.