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

TL;DR

This study investigates the discrepancy in activation gaps in the $ u=1$ quantum Hall state by considering charged impurities, finite width, and Landau level mixing, revealing impurities significantly reduce the gap and skyrmion size.

Contribution

The paper introduces the impact of charged impurities on activation gaps and skyrmion properties, extending previous models that only considered finite width and Landau level mixing.

Findings

Charged impurities significantly reduce the activation gap.

Impurities suppress skyrmion size.

Finite width and LLM alone do not explain the gap discrepancy.

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.