Fractional Quantum Hall Effect in the Second Landau Level: the Importance of Inter-Composite-Fermion Interaction

TL;DR

This paper investigates the fractional quantum Hall effect in the second Landau level, emphasizing the significance of inter-composite-fermion interactions and lambda level mixing, which influence the ground state and excitation gaps.

Contribution

It demonstrates that composite fermion theory with lambda level mixing accurately describes the ground state in the second Landau level, highlighting the importance of inter-fermion interactions.

Findings

Significant differences in states between second and lowest Landau levels.

Composite fermion theory with lambda level mixing reproduces ground states.

Estimated excitation gap at 1/3 filling in second Landau level.

Abstract

Exact diagonalization of a two-dimensional electron gas in a strong magnetic field in the disk geometry shows that there exists a filling factor range in the second Landau level where the states significantly differ from those in the lowest Landau level. We show that the difference arises because the interaction between composite fermions is not negligible in higher Landau levels, as indicated by a substantial mixing between composite-fermion Landau-like levels, or lambda levels. We find that the exact ground state is well reproduced by composite fermion theory with lambda level mixing incorporated at the lowest level of approximation. Using the same variational approach in the spherical geometry we estimate the excitation gap at filling 1/3 in the second Landau level (which corresponds to 7/3 of experiment).