Quantum Hall effect originated from helical edge states in Cd$_3$As$_2$

TL;DR

This paper investigates the origins of the quantum Hall effect in 3D topological semimetals, emphasizing the role of helical edge states and Zeeman splitting in Cd$_3$As$_2$, revealing complex dependencies on experimental parameters.

Contribution

It uncovers a previously ignored Zeeman splitting mechanism of helical edge states contributing to the quantum Hall effect in Cd$_3$As$_2$ slabs.

Findings

Zeeman splitting affects helical edge states and quantum Hall conductance.

Non-monotonic Hall conductance dependence on magnetic field in [112] direction slabs.

Fermi-arc surface states and confinement-induced bulk subbands also influence the effect.

Abstract

The recent experimental observations of the quantum Hall effect in 3D topological semimetals have attracted great attention, but there are still debates on its origin. We systematically study the dependence of the quantum Hall effect in topological semimetals on the thickness, Fermi energy, and growth direction, taking into account the contributions from the Fermi-arc surface states, confinement-induced bulk subbands, and helical side-surface edge states. In particular, we focus on the intensively studied Dirac semimetal Cd$_{3}$As$_{2}$ and its slabs grown along experimentally accessible directions, including [001], [110], and [112]. We reveal an ignored mechanism from the Zeeman splitting of the helical edge states, which along with Fermi-arc 3D quantum Hall effect, may give a non-monotonic dependence of the Hall conductance plateaus on the magnetic field in the most experimentally studied [112] direction slab. Our results will be insightful for exploring the quantum Hall effects beyond two dimensions.