The behavior of the fractional quantum Hall states in the LLL and 1LL with in-plane magnetic field and Landau level mixing: a numerical investigation

TL;DR

This study uses numerical methods to explore how in-plane magnetic fields and Landau level mixing influence fractional quantum Hall states in different Landau levels, revealing anisotropic phases and the effects of LL mixing.

Contribution

It introduces a pseudopotential framework for non-rotationally symmetric interactions and investigates their impact on FQH states in LLL and 1LL.

Findings

Enhancement of 7/3 FQH state with small tilted magnetic field in 1LL.

Monotonic reduction of 1/3 state gap in LLL with increasing in-plane field.

Transition to stripe phase under large tilting and strong anisotropy.

Abstract

By exactly solving the effective two-body interaction for two-dimensional electron system with layer thickness and an in-plane magnetic field, we recently found that the effective interaction can be described by the generalized pseudopotentials (PPs) without the rotational symmetry. With this pseudopotential description, we numerically investigate the behavior of the fractional quantum Hall (FQH) states both in the lowest Landau level (LLL) and first Landau level (1LL). The enhancements of the 7/3 FQH state on the 1LL for a small tilted magnetic field are observed when layer thickness is larger than some critical values. While the gap of the 1/3 state in the LLL monotonically reduced with increasing the in-plane field. From the static structure factor calculation, we find that the systems are strongly anisotropic and finally enter into a stripe phase with a large tilting. With considering the Landau level mixing correction on the two-body interaction, we find the strong LL mixing cancels the enhancements of the FQH states in the 1LL.