Fractional Quantum Hall Effect Based on Weyl Orbits

TL;DR

This paper theoretically demonstrates the possibility of fractional quantum Hall states emerging in three-dimensional Weyl semimetals under magnetic fields, revealing novel topological phases with unique surface localization and fractional Chern numbers.

Contribution

It introduces a new mechanism for fractional quantum Hall states in 3D Weyl semimetals based on Weyl orbit Landau levels and Coulomb interactions, extending 2D topological phenomena.

Findings

Fractional quantum Hall states can form in Weyl semimetals at one-third Landau level filling.

Ground states exhibit a fractional Chern number of 1/3 and uniform electron occupation.

States are localized on surfaces with Fermi arcs and resemble Laughlin states.

Abstract

The fractional quantum Hall effect is a well-known demonstration of strongly correlated topological phases in two dimensions. However, the extension of this phenomenon into a three-dimensional context has yet to be achieved. Recently, the three-dimensional integer quantum Hall effect based on Weyl orbits has been experimentally observed in a topological semimetallic material under a magnetic field. This motivates us to ask whether the Weyl orbits can give rise to the fractional quantum Hall effect when their Landau level is partially filled in the presence of interactions. Here we theoretically demonstrate that the fractional quantum Hall states based on Weyl orbits can emerge in a Weyl semimetal when a Landau level is one-third filled. Using concrete models for Weyl semimetals in magnetic fields, we project the Coulomb interaction onto a single Landau level from the Weyl orbit and find that the ground state of the many-body Hamiltoian is triply degenerate. We further show that the ground states exhibit the many-body Chern number of $1/3$ and the uniform occupation of electrons in both momentum and real space, implying that they are the fractional quantum Hall states. In contrast to the two-dimensional case, the states are spatially localized on two surfaces hosting Fermi arcs. Additionally, our findings suggest that the excitation properties of these states resemble those of the Laughlin state in two dimensions, as inferred from the particle entanglement spectrum of the ground states.