Apparent inconsistency between Streda formula and Hall conductivity in reentrant integer quantum anomalous Hall effect in twisted MoTe$_2$

TL;DR

This paper investigates the discrepancy between Hall conductivity measurements and the Streda formula in reentrant integer quantum anomalous Hall states in twisted MoTe2, proposing explanations involving phase transitions and Fermi surface changes.

Contribution

It offers a novel interpretation of the Hall conductivity discrepancy by linking it to phase transitions and Fermi surface topology in twisted MoTe2.

Findings

Discrepancy explained by quantum Hall bubble or Wigner crystal phase.

Resistive peak indicates a phase transition near ν = -0.75.

Evidence suggests a change in Fermi-surface topology.

Abstract

Recent experiments in twisted bilayer MoTe$_2$ (tMoTe$_2$) have uncovered a rich landscape of correlated phases. In this work, we investigate the reentrant integer quantum anomalous Hall (RIQAH) states reported by F. Xu, arXiv.2504.06972 which display a notable mismatch between the Hall conductivity measured via transport and that inferred from the Streda formula. We argue that this discrepancy can be explained if the RIQAH state is a quantum Hall bubble or Wigner crystal phase, analogous to similar well-established phenomena in two-dimensional (2D) GaAs quantum wells. While this explains the RIQAH state at filling $\nu = -0.63$, F. Xu et al. report that the other RIQAH state at $\nu = -0.7$ has a smaller slope, necessitating a different interpretation. We propose and substantiate with analysis of the experimental data that this discrepancy arises due to a nearby resistive peak masking the true slope. Furthermore, we identify this resistive peak as a signature of a phase transition near $\nu = -0.75$, possibly driven by a van Hove singularity. The anomalous Hall response and Landau fan evolution across this transition suggest a change in Fermi-surface topology and a metallic phase with a non quantized Hall response. These observations offer new insights into the nature of the RIQAH states and raise the possibility that the nearby superconducting phase may have a valley-imbalanced metal parent state.