Interfacial ferroelectricity is a recently established mechanism for generating spontaneous reversible electric polarization, arising from the charge transfer between stacked van der Waals layered atomic crystals. It has been realized in both naturally formed multilayer crystals and moiré superlattices. Owing to the large number of material choices and combinations, this approach is highly versatile, greatly expanding the scope of ultrathin ferroelectrics. A key advantage of interfacial ferroelectricity is its potential to couple with preexisting properties of the constituent layers, enabling their electrical manipulation through ferroelectric switching and paving the way for advanced device functionalities. This review article summarizes recent experimental progress in interfacial ferroelectricity, with an emphasis on its coupling with a variety of electronic properties. After introducing the underlying mechanism of interfacial ferroelectricity and the range of material systems discovered to date, we highlight selected examples showcasing ferroelectric control of excitonic optical properties, Berry curvature effects, and superconductivity. We also discuss the challenges and opportunities that await further studies in this field.

Semiconductor moiré superlattices provide great platforms for exploring exotic collective excitations. Optical Stark effect, a shift of the electronic transition in the presence of a light field, provides an ultrafast and coherent method of manipulating matter states, which, however, has not been demonstrated in moiré materials. Here, we report the valley-selective optical Stark effect of moiré excitons in the WSe$_{2}$/WS$_{2}$ superlattice by using transient reflection spectroscopy. Prominent valley-selective energy shifts up to 7.8 meV have been observed for moiré excitons, corresponding to pseudo-magnetic fields as large as 34 T. Our results provide a route to coherently manipulate exotic states in moiré superlattices.

We theoretically investigated the chiral phonons of honeycomb-type bilayer Wigner crystals recently discovered in van der Waals structures of layered transition metal dichalcogenides. These chiral phonons can emerge under the inversion symmetry breaking introduced by an effective mass imbalance between the two layers or a moiré potential in one layer, as well as under the time-reversal symmetry breaking realized by applying a magnetic field. Considering the wide tunability of layered materials, the frequencies and chirality of phonons can both be tuned by varying the system parameters. These findings suggest that bilayer honeycomb-type Wigner crystals can serve as an exciting new platform for studying chiral phonons.

Moiré systems have emerged as an ideal platform for exploring interaction effects and correlated states. However, most of the experimental systems are based on either triangular or honeycomb lattices. In this study, based on the self-consistent Hartree-Fock calculation, we investigate the phase diagram of the kagomé lattice in a recently discovered system with two degenerate $\varGamma$ valley orbitals and strong spin-orbit coupling. By focusing on the filling factors of $1/2$, $1/3$ and $2/3$, we identify various symmetry-breaking states by adjusting the screening length and dielectric constant. At the half filling, we discover that the spin-orbit coupling induces Dzyaloshinskii-Moriya interaction and stabilizes a classical magnetic state with $120^\circ$ ordering. Additionally, we observe a transition to a ferromagnetic state with out-of-plane ordering. In the case of $1/3$ filling, the system is ferromagnetically ordered due to the lattice frustration. Furthermore, for $2/3$ filling, the system exhibits a pinned droplet state and a $120^\circ$ magnetic ordered state at weak and immediate coupling strengths, respectively. For the strong coupling case, when dealing with non-integer filling, the system is always charge ordered with sublattice polarization. Our study serves as a starting point for exploring the effects of correlation in moiré kagomé systems.

Moiré superlattices provide a new platform to engineer various many-body problems. In this work, we consider arrays of quantum dots (QD) realized on semiconductor moiré superlattices with a deep moiré potential. We diagonalize single QD with multiple electrons, and find degenerate ground states serving as local degrees of freedom (qudits) in the superlattice. With a deep moiré potential, the hopping and exchange interaction between nearby QDs become irrelevant, and the direct Coulomb interaction of the density-density type dominates. Therefore, nearby QDs must arrange the spatial densities to optimize the Coulomb energy. When the local Hilbert space has a two-fold orbital degeneracy, we find that a square superlattice realizes an anisotropic $XY$ model, while a triangular superlattice realizes a generalized $XY$ model with geometric frustration.

Moiré superlattices have revolutionized the study of two-dimensional materials, enabling unprecedented control over their electronic, magnetic, optical, and mechanical properties. This review provides a comprehensive analysis of the latest advancements in moiré physics, focusing on the formation of moiré superlattices due to rotational misalignment or lattice mismatch in two-dimensional materials. These superlattices induce flat band structures and strong correlation effects, leading to the emergence of exotic quantum phases, such as unconventional superconductivity, correlated insulating states, and fractional quantum anomalous Hall effects. The review also explores the underlying mechanisms of these phenomena and discusses the potential technological applications of moiré physics, offering insights into future research directions in this rapidly evolving field.

In recent years, there has been a surge of interest in higher-order topological phases (HOTPs) across various disciplines within the field of physics. These unique phases are characterized by their ability to harbor topological protected boundary states at lower-dimensional boundaries, a distinguishing feature that sets them apart from conventional topological phases and is attributed to the higher-order bulk-boundary correspondence. Two-dimensional (2D) twisted systems offer an optimal platform for investigating HOTPs, owing to their strong controllability and experimental feasibility. Here, we provide a comprehensive overview of the latest research advancements on HOTPs in 2D twisted multilayer systems. We will mainly review the HOTPs in electronic, magnonic, acoustic, photonic and mechanical twisted systems, and finally provide a perspective of this topic.

Two-dimensional (2D) moiré superlattices with a small twist in orientation exhibit a broad range of physical properties due to the complicated intralayer and interlayer interactions modulated by the twist angle. Here, we report a metal-semiconductor phase transition in homojunction moiré superlattices of NiS$_{2}$ and PtTe$_{2}$ with large twist angles based on high-throughput screening of 2D materials $MX_{2 }$ ($M ={\rm Ni}$, Pd, Pt; $X ={\rm S}$, Se, Te) via density functional theory (DFT) calculations. Firstly, the calculations for different stacking configurations (AA, AB and AC) reveal that AA stacking ones are stable for all the bilayer $MX_{2}$. The metallic or semiconducting properties of these 2D materials remain invariable for different stacking without twisting except for NiS$_{2}$ and PtTe$_{2}$. For the twisted configurations, NiS$_{2}$ transfers from metal to semiconductor when the twist angles are 21.79$^\circ$, 27.79$^\circ$, 32.20$^\circ$ and 60$^\circ$. PtTe$_{2}$ exhibits a similar transition at 60$^\circ$. The phase transition is due to the weakened d-p orbital hybridization around the Fermi level as the interlayer distance increases in the twisted configurations. Further calculations of untwisted bilayers with increasing interlayer distance demonstrate that all the materials undergo metal-semiconductor phase transition with the increased interlayer distance because of the weakened d-p orbital hybridization. These findings provide fundamental insights into tuning the electronic properties of moiré superlattices with large twist angles.

Recent advancements in two-dimensional van der Waals moiré materials have unveiled the captivating landscape of moiré physics. In twisted bilayer graphene (TBG) at `magic angles', strong electronic correlations give rise to a diverse array of exotic physical phenomena, including correlated insulating states, superconductivity, magnetism, topological phases, and the quantum anomalous Hall (QAH) effect. Notably, the QAH effect demonstrates substantial promise for applications in electronic and quantum computing devices with low power consumption. This article focuses on the latest developments surrounding the QAH effect in magic-angle TBG. It provides a comprehensive analysis of magnetism and topology - two crucial factors in engineering the QAH effect within magic-angle TBG. Additionally, it offers a detailed overview of the experimental realization of the QAH effect in moiré superlattices. Furthermore, this review highlights the underlying mechanisms driving these exotic phases in moiré materials, contributing to a deeper understanding of strongly interacting quantum systems and facilitating the manipulation of new material properties to achieve novel quantum states.

Two-dimensional (2D) van der Waals (vdW) moiré superlattices have attracted significant attention due to their novel physical properties and quantum phenomena. The realization of these fascinating properties, however heavily depends on the quality of the measured moiré superlattices, emphasizing the importance of advanced fabrication techniques. This review provides an in-depth discussion of the methods for fabricating moiré superlattices. It begins with a brief overview of the structure, properties, and potential applications of moiré superlattices, followed by a detailed examination of fabrication techniques, focuses on different kinds of transfer techniques and growth methods, particularly chemical vapor deposition (CVD) method. Finally, it addresses current challenges in fabricating high-quality moiré superlattices and discusses potential directions for future advancements in this field. This review will enhance the understanding of moiré superlattice fabrication and contributing to the continued development of 2D twistronics.

Determining the electronic structure of La$_3$Ni$_2$O$_7$ is an essential step towards uncovering its superconducting mechanism. It is widely believed that the bilayer apical oxygens play an important role in the bilayer La$_3$Ni$_2$O$_7$ electronic structure. Applying the hybrid exchange-correlation functionals, we obtain a more accurate electronic structure of La$_3$Ni$_2$O$_7$ at its high-pressure phase, where the bonding $\mathrm{d}_{z^2}$ band is below the Fermi level owing to the apical oxygen. The symmetry properties of this electronic structure and its corresponding tight-binding model are further analyzed. We find that the antisymmetric part is highly entangled, leading to a minimal nearly degenerate two-orbital model. Then, the apical oxygen vacancies effect is studied using the dynamical cluster approximation. This disorder effect strongly destroys the antisymmetric $\beta$ Fermi surface, leading to the possible disappearance of superconductivity.