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

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.