Fractional quantum Hall effect of topological surface states under a strong tilted magnetic field

TL;DR

This paper theoretically investigates the fractional quantum Hall effect on topological surface states under a strong tilted magnetic field, revealing how tilt angle influences state stability and excitation gaps.

Contribution

It provides analytical pseudopotentials and demonstrates how in-plane magnetic field components affect FQHE stability and excitation gaps in topological surface states.

Findings

FQHE state stability increases at n=0 LL with tilt angle.

Excitation gaps at ν=1/3 increase as tilt angle increases.

Stabilities of n=±1 LLs decrease with tilt angle.

Abstract

The fractional quantum Hall effect (FQHE) of topological surface-state particles under a tilted strong magnetic field is theoretically studied by using the exact diagonalization method. The Haldane's pseudopotentials for the Coulomb interaction are analytically obtained. The results show that by increasing the in-plane component of the tilted magnetic field, the FQHE state at $n$=0 Landau level (LL) becomes more stable, while the stabilities of $n$=$\pm1$ LLs become weaker. Moreover, we find that the excitation gaps of the $\nu=1/3$ FQHE states increase as the tilt angle is increased.