Fractional quantum Hall effect in a tilted magnetic field

TL;DR

This paper investigates how tilting a magnetic field affects the fractional quantum Hall states in quantum wells, revealing phase transitions and the role of geometrical degrees of freedom.

Contribution

It provides a detailed phase diagram showing the transition from fractional quantum Hall fluid to stripe phases under tilted magnetic fields.

Findings

Fractional quantum Hall fluid persists under moderate tilts.

Transition to stripe phase occurs at higher tilt angles.

Tilting probes geometrical aspects of quantum Hall states.

Abstract

We discuss the orbital effect of a tilted magnetic field on the quantum Hall effect in parabolic quantum wells. Many-body states realized at the fractional 1/3 and 1/2 filling of the second electronic subband are studied using finite-size exact diagonalization. In both cases, we obtain the phase diagram consisting of a fractional quantum Hall fluid phase that persists for moderate tilts, and eventually undergoes a direct transition to the stripe phase. It is shown that tilting of the field probes the geometrical degree of freedom of fractional quantum Hall fluids, and can be partly related to the effect of band-mass anisotropy.