Quantum Phases in Twisted Homobilayer Transition Metal Dichalcogenides

TL;DR

Twisted TMD homobilayers such as tMoTe2 and tWSe2 host narrow, topologically nontrivial moiré bands whose strong Coulomb interactions drive a spectrum of integer and fractional topological states as well as superconductivity without external magnetic fields. The topology emerges from valley-contrasted Berry curvature and emergent skyrmion textures that produce an effective field B_eff, enabling Haldane-like physics in a single valley and Kane-Mele physics when both valleys are included. Experiments reveal IQAH and FQAH insulators, IQSH states, zero-field composite Fermi liquids, anomalous Hall metals, and superconductivity, with phase formation tunable via carrier density, displacement field, twist angle, and magnetic field. The field holds promise for gate-defined topological devices and exploring non-Abelian fractional phases, but key challenges remain, including direct anyon detection and understanding superconducting pairing across different twist-angle regimes.

Abstract

Twisted homobilayer transition metal dichalcogenides - specifically twisted bilayer MoTe$_2$ and twisted bilayer WSe$_2$ - have recently emerged as a versatile platform for strongly correlated and topological phases of matter. These two-dimensional systems host tunable flat Chern bands in which Coulomb interactions can dominate over kinetic energy, giving rise to a variety of interaction-driven phenomena. A series of groundbreaking experiments have revealed a rich landscape of quantum phases, including integer and fractional quantum anomalous Hall states, quantum spin Hall states, anomalous Hall metals, zero-field composite Fermi liquids, and unconventional superconductors, along with more conventional topologically trivial correlated states including antiferromagnets. This review surveys recent experimental discoveries and theoretical progress in understanding these phases, with a focus on the key underlying mechanisms - band topology, electron interactions, symmetry breaking, and charge fractionalization. We emphasize the unique physics of twisted TMD homobilayers in comparison to other related systems, discuss open questions, and outline promising directions for future research.

Figures (5)

• Figure 1: Single-particle physics in twisted homobilayer TMDs. (a) Moiré superlattices of $R$-stacked twisted homobilayers. The dots identify the high symmetry positions $\mathcal{R}_M^M$, $\mathcal{R}_X^M$, and $\mathcal{R}_M^X$, and the solid lines outline a single moiré unit cell. (b) Brillouin zones of the bottom (blue) and top (red) layers in a twisted bilayer, and the moiré Brillouin zone (black). (c) Moiré band states near the valence band maxima of two valleys. The color shading indicates the degree of layer polarization of the corresponding layer spinors (bottom=blue and top=red). (d) Map of the skyrmion field $n(\boldsymbol{r})$ and (e) the corresponding effective magnetic field $B_{\mathrm{eff}}(\boldsymbol{r})$ of $t$MoTe$_2$ at $\theta= 3.8^\circ$. The black hexagon in (d) (the white hexagon in (e)) is the Wigner-Seitz cell of the moiré superlattice. (f) Moiré band structure of $t$MoTe$_2$ at $\theta= 3.8^\circ$ calculated from the continuum model. The numbers $(+1,-1,0)$ are the Chern numbers of the first three moiré valence bands. (g) The honeycomb lattice formed by $\mathcal{R}_X^M$, and $\mathcal{R}_M^X$ sites. Red and orange dashed arrows indicate the phase pattern of next-nearest-neighbor hopping in the effective Haldane model for the first two bands in (f). Panels (a)-(c) are adapted from Ref. Pan2020Band.
• Figure 2: Schematic phase diagram of $t$MoTe$_2$ as a function of hole filling $\nu_h$ and displacement field. This phase diagram summarizes experimental observations in Refs. Anderson2023ProgrammingCai2023Zeng2023Park2023Xu2023ObservationPark2025FerromagnetismXu2025InterplayXu2025signatureskang2024evidence across twist angles ranging from $2.1^{\circ}$ to $3.9^{\circ}$. Some of the phases appear only at certain devices and twist angles. For example, the superconductor (SC) around $\nu_h \approx 0.73$ has so far been reported only in a device of $t$MoTe$_2$ with $\theta=3.83^{\circ}$Xu2025signatures. Evidence of an FQSH insulator has been reported in $t$MoTe$_2$ with $\theta=2.1^{\circ}$kang2024evidence. (FM metal refers to ferromagnetic metals.)
• Figure 3: Superconductivity and topological phases observed in $t$WSe$_2$. (a) A map of longitudinal resistance $R$ is plotted as a function of density and displacement field at $T=200\,\mathrm{mK}$ in $t$WSe$_2$ at $\theta=5.0^\circ$. (b) A schematic phase diagram of superconductor (SC) and antiferromagnetic (AFM) phases based on (a). Both (a) and (b) are adapted from Ref. Guo2025Superconductivity. (c) Experimental observation of superconductivity in $t$WSe$_2$ at $\theta=3.65^\circ$, reported by Ref. Xia2025Superconductivity. The plot shows the longitudinal resistance $R$ as a function of hole filling factor and applied electrical field with temperature $T=50\,\mathrm{mK}$. The region with zero resistance is marked by a dashed line. (d) Experimental phase diagram of the IQAH insulator at $\nu_h = 1$ as function of $\theta$ and effective displacement field $D_{\text{eff}}$ from Ref. Foutty2024Mapping. Red regions mark the IQAH phase, while black regions represent the topologically trivial phase.
• Figure 4: Competing topological and magnetic phases at $\nu_h = 1$. (a) Quantum phase diagram at $\nu_h = 1$ as a function of displacement potential $V_z$ and twist angle $\theta$. The color map represents the layer polarization $P$. (b) The $\nu_h = 1$ mean-field band structure at $\theta = 3.4^\circ$ and $V_z=0\,\mathrm{meV}$ for the integer quantum anomalous Hall insulator (QAHI). The solid (dashed) lines plot bands in the $+K$ ($-K$) valley, and the horizontal black dashed line indicates the chemical potential centered in the interaction-induced gap. The color denotes the layer polarization of Bloch states, which varies dramatically across the moiré Brillouin zone at energies above the chemical potential, indicating the winding of layer pseudospin. (c) Schematic illustration of the four $120^\circ$ antiferromagnetic states in (a) with different spatial occupations and spin vector chiralities. The red, orange, and cyan dots represent the $\mathcal{R}_M^X$, $\mathcal{R}_X^M$, and $\mathcal{R}_M^M$ sites in the moiré superlattices. $\text{AF}^{\pm}$ denote antiferromagnetic states with $\pm$ spin vector chirality. This figure is adapted from Ref. Li2024Electrically.
• Figure 5: Numerical results in the first moiré valence band of $t$MoTe$_2$ for fractionalized states. (a-b) Berry curvature $\Omega_{\boldsymbol{k}}$ and trace of quantum metric $\mathrm{Tr} g_{\boldsymbol{k}}$ at $\theta = 2.9^\circ$ in the moiré Brillouin zone. (c) Deviation $T$ from ideal quantum geometry and Laudau level weight $W$ as functions of $\theta$. (d) Map of $|\mathcal{B}(\boldsymbol{r})|$ scaled by its spatial average at $\theta = 2.9^\circ$. (e) ED spectra based on $\varphi_{1,\boldsymbol{k}}$ (blue lines) and $\Theta_{\boldsymbol k}(\boldsymbol r)$ (red dots) at $\nu_h = 2/3$ and $\theta = 3.7^\circ$. (f) Infinite DMRG results of the composite Fermi liquid (CFL) at $\nu_h = 1/2$ and $\theta = 3.7^\circ$. The left panel shows the occupations $n(\boldsymbol{k})$ in the Brillouin zone, comparing the Fermi liquid (left side) and the CFL (right side). The right panel presents the connected structure factor $S(\boldsymbol{q}) = \langle \hat{\rho}_{\boldsymbol{q}} \hat{\rho}_{-\boldsymbol{q}} \rangle - \langle \hat{\rho}_{\boldsymbol{q}} \rangle \langle \hat{\rho}_{-\boldsymbol{q}} \rangle$. Panels (a)-(e) are adapted from Ref. li2025variational, and panel (f) is from Ref. Dong2023.