Wigner Crystalization in the Lowest Landau Level for $\nu \ge 1/5$

TL;DR

This study uses exact diagonalization to investigate the ground states of seven electrons in the lowest Landau level, revealing Wigner crystal formation between filling factors 1/3 and 1/5 under Coulomb interactions.

Contribution

It demonstrates that Wigner crystals are the ground state in this regime and clarifies the role of pseudopotential parameters in the Landau level.

Findings

Wigner crystal is the ground state between ν=1/3 and ν=1/5 with Coulomb interaction.

At ν=1/5, the Wigner crystal has lower energy than the Laughlin state.

The gapless state from suppressed short-range interactions is unrelated to Wigner crystallization.

Abstract

By means of exact diagonalization we study the low-energy states of seven electrons in the lowest Landau level which are confined by a cylindric external potential modelling the rest of a macroscopic system and thus controlling the filling factor $\nu $. Wigner crystal is found to be the ground state for filling factors between $ \nu = 1/3$ and $ \nu = 1/5$ provided electrons interact via the bare Coulomb potential. Even at $\nu =1/5$ the solid state has lower energy than the Laughlin's one, although the two energies are rather close. We also discuss the role of pseudopotential parameters in the lowest Landau level and demonstrate that the earlier reported gapless state, appearing when the short-range part of the interaction is suppressed, has nothing in common with the Wigner crystalization in pure Coulomb case.