Electron correlation and topology are two central threads of modern condensed matter physics. Semiconductor moire materials provide a highly tunable platform for studies of electron correlation. Correlation-driven phenomena, including the Mott insulator, generalized Wigner crystals, stripe phases and continuous Mott transition, have been demonstrated. However, nontrivial band topology has remained elusive. Here we report the observation of a quantum anomalous Hall (QAH) effect in AB-stacked MoTe2/WSe2 moire heterobilayers. Unlike in the AA-stacked structures, an out-of-plane electric field controls not only the bandwidth but also the band topology by intertwining moire bands centered at different high-symmetry stacking sites. At half band filling, corresponding to one particle per moire unit cell, we observe quantized Hall resistance, h/e2 (with h and e denoting the Planck's constant and electron charge, respectively), and vanishing longitudinal resistance at zero magnetic field. The electric-field-induced topological phase transition from a Mott insulator to a QAH insulator precedes an insulator-to-metal transition; contrary to most known topological phase transitions, it is not accompanied by a bulk charge gap closure. Our study paves the path for discovery of a wealth of emergent phenomena arising from the combined influence of strong correlation and topology in semiconductor moire materials.

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Quantum anomalous Hall effect from intertwined moiré bands

Semiconductor moiré materials

A grand family of two-dimensional (2D) materials and their heterostructures have been discovered through the extensive experimental and theoretical efforts of chemists, material scientists, physicists, and technologists. These pioneering works contribute to realizing the fundamental platforms to explore and analyze new physical/chemical properties and technological phenomena at the micro-nano-pico scales. Engineering 2D van der Waals (vdW) materials and their heterostructures via chemical and physical methods with a suitable choice of stacking order, thickness, and interlayer interactions enable exotic carrier dynamics, showing potential in high-frequency electronics, broadband optoelectronics, low-power neuromorphic computing, and ubiquitous electronics. This comprehensive review addresses recent advances in terms of representative 2D materials, the general fabrication methods, and characterization techniques and the vital role of the physical parameters affecting the quality of 2D heterostructures. The main emphasis is on 2D heterostructures and 3D-bulk (3D) hybrid systems exhibiting intrinsic quantum mechanical responses in the optical, valley, and topological states. Finally, we discuss the universality of 2D heterostructures with representative applications and trends for future electronics and optoelectronics (FEO) under the challenges and opportunities from physical, nanotechnological, and material synthesis perspectives.

2D Heterostructures for Ubiquitous Electronics and Optoelectronics: Principles, Opportunities, and Challenges.

Moir\'e materials with flat electronic bands provide a highly controllable quantum system for studies of strong-correlation physics and topology. In particular, angle-aligned heterobilayers of semiconducting transition metal dichalcogenides (TMDs) with large band offset realize the single-band Hubbard models. Introduction of a new layer degree of freedom is expected to foster richer interactions, enabling Hund's physics, interlayer exciton condensation and new superconducting pairing mechanisms to name a few. Here, we report competing electronic orders in twisted AB-homobilayer WSe2, which realizes a bilayer Hubbard model in the weak interlayer hopping limit for holes. We characterize the charge order, layer polarization and magnetization of the moir\'e bilayer, subjected to an out-of-plane electric and magnetic field, by exciton sensing and magneto circular dichroism measurements. By layer-polarizing holes via the electric field, we observe a crossover from an excitonic insulator to a charge-transfer insulator at hole density of $\nu$=1 (in unit of moir\'e density), a transition from a paramagnetic to an antiferromagnetic charge-transfer insulator at $\nu$=2, and evidence for a layer-selective Mott insulator at 1<$\nu$<2. The unique coupling of charge and spin to external fields also manifests a giant magneto-electric response. Our results establish a new solid-state simulator for problems in strong-correlation physics that are described by bilayer Hubbard models. 

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A tunable bilayer Hubbard model in twisted WSe2

Many-body interactions between carriers lie at the heart of correlated physics. The ability to tune such interactions would allow the possibility to access and control complex electronic phase diagrams. Recently, two-dimensional moiré superlattices have emerged as a promising platform for quantum engineering such phenomena1-3. The power of the moiré system lies in the high tunability of its physical parameters by adjusting the layer twist angle1-3, electrical field4-6, moiré carrier filling7-11 and interlayer coupling12. Here we report that optical excitation can highly tune the spin-spin interactions between moiré-trapped carriers, resulting in ferromagnetic order in WS2 /WSe2 moiré superlattices. Near the filling factor of -1/3 (that is, one hole per three moiré unit cells), as the excitation power at the exciton resonance increases, a well-developed hysteresis loop emerges in the reflective magnetic circular dichroism signal as a function of magnetic field, a hallmark of ferromagnetism. The hysteresis loop persists down to charge neutrality, and its shape evolves as the moiré superlattice is gradually filled, indicating changes of magnetic ground state properties. The observed phenomenon points to a mechanism in which itinerant photoexcited excitons mediate exchange coupling between moiré-trapped holes. This exciton-mediated interaction can be of longer range than direct coupling between moiré-trapped holes9, and thus magnetic order arises even in the dilute hole regime. This discovery adds a dynamic tuning knob to the rich many-body Hamiltonian of moiré quantum matter13-19. 

Light-induced ferromagnetism in moiré superlattices

In moir\'e heterostructures, gate-tunable insulating phases driven by electronic correlations have been recently discovered. Here, we use transport measurements to characterize the gate-driven metal-insulator transitions and the metallic phase in twisted WSe$_2$ near half filling of the first moir\'e subband. We find that the metal-insulator transition as a function of both density and displacement field is continuous. At the metal-insulator boundary, the resistivity displays strange metal behaviour at low temperature with dissipation comparable to the Planckian limit. Further into the metallic phase, Fermi-liquid behaviour is recovered at low temperature which evolves into a quantum critical fan at intermediate temperatures before eventually reaching an anomalous saturated regime near room temperature. An analysis of the residual resistivity indicates the presence of strong quantum fluctuations in the insulating phase. These results establish twisted WSe$_2$ as a new platform to study doping and bandwidth controlled metal-insulator quantum phase transitions on the triangular lattice.

Quantum Criticality in Twisted Transition Metal Dichalcogenides

Near the boundary between ordered and disordered quantum phases, several experiments have demonstrated metallic behaviour that defies the Landau Fermi paradigm1–5. In moire heterostructures, gate-tuneable insulating phases driven by electronic correlations have been recently discovered6–23. Here, we use transport measurements to characterize metal–insulator transitions (MITs) in twisted WSe2 near half filling of the first moire subband. We find that the MIT as a function of both density and displacement field is continuous. At the metal–insulator boundary, the resistivity displays strange metal behaviour at low temperatures, with dissipation comparable to that at the Planckian limit. Further into the metallic phase, Fermi liquid behaviour is recovered at low temperature, and this evolves into a quantum critical fan at intermediate temperatures, before eventually reaching an anomalous saturated regime near room temperature. An analysis of the residual resistivity indicates the presence of strong quantum fluctuations in the insulating phase. These results establish twisted WSe2 as a new platform to study doping and bandwidth-controlled metal–insulator quantum phase transitions on the triangular lattice. Metal-to-insulator transitions are characterized in twisted WSe, revealing strange metal behaviour and quantum criticality at low temperatures.

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Giancarlo S. S. G. Pereira

Papers

Quantum Criticality in Twisted Transition Metal Dichalcogenides

Quantum criticality in twisted transition metal dichalcogenides.