Fixed-phase diffusion Monte Carlo study of the activation gap and the skyrmion excitation of $\nu=1$ system in the presence of charged impurities

Abstract

The discrepancy between the theoretically calculated and experimentally measured activation gaps in quantum Hall effect has long been a puzzle. We revisit this issue in the context of the $\nu=1$ quantum Hall state, while also incorporating the skyrmion physics. We find that the finite width and the Landau level mixing (LLM) effects are not sufficient to explain the observed activation gap. We further show that the presence of charged impurities located adjacent to the quantum well can cause a significant reduction in the activation gap, while also causing a suppression of the skyrmion size.