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

TL;DR

The paper addresses why the Hall response inferred from the Streda slope disagrees with transport measurements in reentrant integer quantum anomalous Hall states observed in twisted MoTe$_2$. It proposes that a quantum Hall bubble or Wigner crystal phase on top of a quantized IQAH background can explain the RIQAH2 state and may account for the RIQAH1 mismatch if a nearby resistive peak masks the true slope; a VHS-driven transition near $ν\approx -0.75$ is implicated in this peak. A van Hove singularity near $ν=-0.83$ in a valley-unpolarized metal provides a mechanism for a Stoner-type transition and a Fermi-surface topology change, aligning with changes in $ρ_{xy}$ and the emergence of a nearby superconducting phase. Together, these results offer a coherent framework for RIQAH physics in moiré TMDs, highlight the role of short-range disorder in stabilizing electron solids, and propose concrete experiments to test the bubble/WC scenario and its connection to superconductivity.

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 $ν= -0.63$, F. Xu et al. report that the other RIQAH state at $ν= -0.7$ 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 $ν= -0.75$, 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.

Figures (4)

• Figure 1: The experimental longitudinal and Hall resistivity, $\rho_{xx}$ and $\rho_{xy}$, respectively, of the sample from Ref. xu_signatures_2025 are plotted in panels (a) and (b). Both are plotted as a function of magnetic flux per unit cell, $\phi$, and filling per unit cell, $\nu$. The vertical scale $\phi$ of all plots is identical, with tick marks provided for visual aid. Data are taken at a temperature of $15$mK and zero displacement field. We have added labels to a few features. The IQAH state has vanishing $\rho_{xx} \ll h/e^2$ and quantized $\rho_{xy} \approx h/e^2$. The anomalous Hall metal (AHM) appears across a resistive $\rho_{xx}$ peak. At small magnetic field it has larger $\rho_{xx}$ than the IQAH state and nearly zero $\rho_{xy} \ll \rho_{xx} \ll h/e^2$. At larger magnetic fields a Landau fan emanating from $\nu = -1$ becomes apparent. Feature (1) corresponds to the first reentrant integer quantum anomalous Hall (RIQAH1) state, characterized by low $\rho_{xx}$ and quantized $\rho_{xy} \approx h/e^2$. This RIQAH1 state terminates before reaching $B = 0$ due to the emergence of SC, a putative superconducting phase. There is a second RIQAH state at feature (2), RIQAH2. In panel (c) the longitudinal resistivity is again plotted, but now with selected resistivity minima and maxima extracted. Appendix \ref{['app:line_fitting']} details the process of extracting these minima and maxima and fitting to the white lines. Here solid white lines are fits where the slope is equal to the intercept, and dotted white lines are fits where they are not. We show RIQAH1 and RIQAH2, highlighted by the markers (1) and (2) and orange and cyan points, respectively. For reference we also show the FQAH states at $-2/3$ and $-3/5$, highlighted by the FQAH markers and pink and tan points, respectively. We find that both FQAH state and the RIQAH2 state are well fit by lines with intercepts equal to their slopes. This can be seen in the small difference between the dotted and solid fits. However, the RIQAH1 state is not, as shown by the large difference between the dotted and solid fit. We expect this is because the slope of the nearby resistivity peak, highlighted by red points, corresponds to $C=-0.49\pm 0.08$, which may obscure the slope of RIQAH1. For more details on the slopes of the fits see Table \ref{['tab:streda_and_transport']}.
• Figure 2: Schematics of the bubble or Wigner crystal phase + IQAH background. (a) The bubble or Wigner crystal phase involves electrons of a fixed fraction $p_B$ of the IQAH background that forms a lattice pinned by disorder. (b) Schematic of flux $\phi$ versus filling $\nu$. The lines indicate the center of $\rho_{xx}$ minima which shift as a function of $\phi$ and $\nu$ giving rise to the Streda slope. For a lattice system with an integer Chern band, the Berry curvature at $B = 0$ mimics a background magnetic field, which intercepts the conventional Landau fan at $1/C$ flux quantum, illustrated by the dashed lines.
• Figure 3: Single-particle density of states and experimental resistance as functions of doping, $\nu$. (a) The single particle density of states (DOS) for valley unpolarized tMoTe$_2$ at a twist angle of $3.8^{\circ}$. A DOS peak can be observed at the VHS at $\nu = -0.83$, indicated by the blue dotted line. Plotted in the inset is the single-particle Berry phase in units of $2\pi$ corresponding to a valley polarized Fermi surface. On the $x$ axis the filling runs from $-1$ to $0$ while on the $y$ axis $C$ runs from $-1$ to $0$. The value of $C$ is close to $-0.77$ near $\nu=-0.83$, indicated by the dotted lines. Also shown is the orange dotted line indicating the filling where the peak in resistivity appears, plotted more fully in (b). It can be seen to be close to the location of the VHS. (b) The experimental resistivity, $\rho_{xx}$, from Ref. xu_signatures_2025 at $T=15$mK and $B=5$T is plotted in orange for $-0.9 <\nu <-0.66$. This is the same peak in resistivity highlighted in red markers in Fig. \ref{['fig:streda_one']}(c). Note that the reason for choosing $B=5$T was to avoid the SC state that appears at $B=0$T.
• Figure 4: A plot of the fitting process used to avoid noise in the resistivity minima and maxima. Once candidate minima and maxima were identified parabolas were fit to smooth out any noise near the minima. The plot displays fits of parabolas to two identified minima at $B=1.8$. The leftmost minima corresponds to the FQAH state at $\nu = -2/3$ while the rightmost corresponds to the RIQAH2 state.