Fractional quantum Hall effect in topological insulators: The role of Zeeman effect

TL;DR

This paper investigates how the Zeeman effect influences the fractional quantum Hall effect on topological insulator surfaces, revealing asymmetries in ground state energies and excitation gaps between Landau levels.

Contribution

It demonstrates that Zeeman effect significantly alters pseudopotentials and the robustness of FQHE states in topological insulators, differing from graphene.

Findings

Zeeman effect reforms Coulomb pseudopotentials.

FQHE at n=1 LL is more robust than at n=-1 LL.

Ground state energies and gaps show asymmetry between Landau levels.

Abstract

We study the role of Zeeman effect in fractional quantum Hall effect (FQHE) on the surface of topological insulators (TIs). We show that the effective pseudopotentials of the Coulomb interaction are reformed due to Zeeman effect, which are quite different from those in graphene. By exactly diagonalizing the many-body Hamiltonian in the sphere geometry, we find that the ground state energies and the excitation gaps at $\nu$=1/3 FQHE between the $n$=$\pm1$ Landau levels (LLs) render asymmetry, and the FQHE state at the $n$=1 LL is more robust than that at $n$=-1 LL since the excitation gap at $n$=1 LL is larger than that at $n$=-1 LL.