Inevitable First Order Phase Transitions in 3D Quantum Hall Systems

TL;DR

This paper proposes that in 3D quantum Hall systems, inevitable first order phase transitions driven by Landau level jumps can explain experimental observations without requiring charge density waves, including Hall resistivity plateaus and metal-insulator transitions.

Contribution

It introduces a non-CDW mechanism involving first order phase transitions in 3D metals under strong magnetic fields, explaining experimental phenomena in ZrTe$_5$ and HfTe$_5$.

Findings

First order phase transitions occur at Landau level jumps.

These transitions can cause phase separation and percolation.

The model reproduces Hall resistivity plateaus and metal-insulator transitions.

Abstract

Recent experiments suggest that low carrier density three-dimensional (3D) metals ZrTe$_5$ and HfTe$_5$ exhibit the 3D quantum Hall (QH) effect with Hall resistivity plateaus and a metal-insulator transition in strong magnetic fields. The conventional 3D QH theory requires a fixed period charge density wave (CDW), which is however not observed experimentally. We investigate alternative non-CDW mechanisms by considering a 3D metal in strong magnetic fields with electrons coupled to a boson (e.g., phonon) field. We show that the model exhibits inevitable first order phase transitions at jumps of the number of occupied Landau level bands, which do not involve CDW. These transitions may drive the system into a phase separation state with percolation transitions. We further show this can lead to Hall resistivity quasi-plateaus similar to that observed experimentally, and can provide a natural explanation for the metal-insulator transition.