3D Quantum Hall Effect with Two Distinct Plateaus

TL;DR

This paper explains the second Hall plateau in 3D quantum Hall effect observed in HfTe5 as resulting from a spin-density-wave-induced insulating state caused by a Lifshitz transition of Landau bands.

Contribution

It demonstrates that a magnetic-field-driven Lifshitz transition induces a spin-density wave, leading to a second Hall plateau in 3D quantum Hall systems, expanding understanding beyond 2D effects.

Findings

The second plateau is due to a spin-density-wave insulating state.

A Lifshitz transition causes Landau band crossing and nesting.

Calculated resistivities match experimental observations.

Abstract

The recent discovery of the 3D quantum Hall effect in $\mathrm{HfTe_5}$ has also revealed puzzling signatures of possible 3D fractionalization. Beyond the first plateau associated with the lowest Landau band, Hall conductivity exhibits a second plateau with a value of about $3/5$ of the first, accompanied by a suppressed longitudinal resistivity. Here, we attribute this second plateau to an insulating ground state arising from spin-density-wave order. We show that a magnetic-field-driven Lifshitz transition causes the spin-down holelike zeroth Landau band to cross the Fermi energy and that the resulting nesting between the lowest spin-up and spin-down Landau bands induces a spin-density wave. We calculate the Hall and longitudinal resistivity and reproduce the experimental behaviors. Our renormalization-group analysis further supports this insulating ground state. Our work reveals that the tunability of Landau bands along the magnetic-field direction endows the 3D quantum Hall effect with a broader phenomenology than its 2D counterpart and merits further exploration.