Spin-Orbit Interaction Enhanced Fractional Quantum Hall States in the Second Landau Level

TL;DR

This study investigates how spin-orbit interaction influences the stability of fractional quantum Hall states at specific filling factors in the second Landau level, using numerical methods to analyze energy gaps and correlations.

Contribution

It demonstrates that spin-orbit interaction enhances the stability of fractional quantum Hall states at 7/3 and 5/2 filling factors in the second Landau level.

Findings

Spin-orbit interaction stabilizes fractional quantum Hall states.

Energy gaps are increased by spin-orbit effects.

Pair-correlation functions indicate enhanced correlations.

Abstract

We study the fractional quantum Hall effect at filling fractions 7/3 and 5/2 in the presence of the spin-orbit interaction, using the exact diagonalization method and the density matrix renormalization group (DMRG) method in a spherical geometry. Trial wave functions at these fillings are the Laughlin state and the Moore-Reed-Pfaffian state. The ground state excitation energy gaps and pair-correlation functions at fractional filling factor 7/3 and 5/2 in the second Landau level are calculated. We find that the spin-orbit interaction stabilizes the fractional quantum Hall states.