Hamiltonian theory for Quantum Hall systems in a tilted magnetic field: robustness of activation gaps

TL;DR

This paper uses Hamiltonian theory to analyze the impact of a tilted magnetic field on quantum Hall systems, showing that activation gaps remain robust despite anisotropy introduced by the in-plane field.

Contribution

It introduces a method to incorporate anisotropy via generalized pseudo-potentials and calculates the robustness of activation gaps in tilted magnetic fields.

Findings

Activation gaps are robust against in-plane magnetic fields in the lowest Landau level.

Off-diagonal pseudo-potentials cause Landau level mixing, which can be minimized by adjusting the composite fermion geometry.

The optimal metric for composite fermions can be determined for different tilting angles.

Abstract

We use the Hamiltonian theory developed by Shankar and Murthy to study a quantum Hall system in a tilted magnetic field. With a finite width of the system in the $z$ direction, the parallel component of the magnetic field introduces anisotropy into the effective two-dimensional interactions. The effects of such anisotropy can be effectively captured by the recently proposed generalized pseudo-potentials. We find that the off-diagonal components of the pseudo-potentials lead to mixing of composite fermions Landau levels, which is a perturbation to the picture of $p$ filled Landau levels in composite-fermion theory. By changing the internal geometry of the composite fermions, such a perturbation can be minimized and one can find the corresponding activation gaps for different tilting angles, and we calculate the associated optimal metric. Our results show that the activation gap is remarkably robust against the in-plane magnetic field in the lowest Landau level.