Phase transition and intrinsic metric of the dipolar fermions in quantum Hall regime

TL;DR

This paper investigates how anisotropic dipolar interactions in quantum Hall systems affect fractional quantum Hall states, revealing their robustness, phase transitions, and formation of bound states as the dipole orientation varies.

Contribution

It introduces a generalized pseudopotential expansion for anisotropic dipolar interactions and studies their effects on FQH states using numerical diagonalization.

Findings

FQH states at ν=1/3 and ν=2+1/5 are most stable in isotropic conditions.

FQH states exhibit robustness under dipole angle rotation.

Phase transition to a molecule phase occurs with increasing anisotropy.

Abstract

For the fast rotating quasi-two-dimensional dipolar fermions in the quantum Hall regime, the interaction between two dipoles breaks the rotational symmetry when the dipole moment has component in the the plane via being tuned by an external field. For the anisotropic two-body interaction, we expand it in a generalized pseudopotentials (PPs). With assuming that all the dipoles are polarized in the same direction, we perform the numerical diagonalization for finite size systems on a torus. We find that the most stable fractional quantum Hall (FQH) states in the lowest Landau level (LLL) and the first Landau level (1LL) are {\nu} = 1/3 and {\nu} = 2 + 1/5 Laughlin state respectively in the isotropic case. While rotating the dipolar angle, these FQH states reveal a robustness and finally enter into a molecule phase in which all the particles are attracted and form a bound state. The anisotropy and the phase transition are studied by the intrinsic metric, the wave function overlap and the nematic order parameter.