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

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.