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Electron superlattices provide a powerful way to engineer novel correlated and topological quantum phenomena. Originally lithographic-patterned gate arrays were designed to create periodic superlattices in two-dimensional electron gases (2DEGs), where the superlattice potential can be continuously varied electrically. Fabricating superlattices at the nanometer scale with high precision, however, is challenging lithographically. Recently, moiré patterns in 2D materials have been found to offer near-perfect nanometer-scale electronic superlattices, which led to discoveries of exciting quantum phenomena in a variety of moiré heterostructures. However, the requirement of the moiré pattern poses a stringent limit on the material selection, and the moiré potential is not tunable for a given moiré heterostructure. To better engineer novel quantum phases, it will be desirable to create superlattices that combine the advantages of these two methods. Here we achieve this goal by engineering tunable correlated states in bilayer graphene with a remote Coulomb superlattice. The Coulomb superlattice is realized by localized electrons in a twisted bilayer WS2 that are 3 nm above the bilayer graphene. The period of the Coulomb superlattice is determined by the moiré period of the twisted bilayer WS2, and the strength of the superlattice potential is controlled by the number of localized electrons at the twisted bilayer WS2 moiré lattice site. We demonstrate that the 2DEG in encapsulated bilayer graphene is described by the Fermi liquid when the remote Coulomb superlattice is turned off. Electron correlation increases dramatically when the remote Coulomb superlattice is turned on, resulting in a series of correlated insulating states at both integer and fractional filling factors. This remote Coulomb superlattice can be applied to any 2D materials hosting a 2DEG. It opens a new route for in-situ control of correlated quantum phenomena in a wide variety of 2D systems.

Moire superlattices in transition metal dichalcogenide (TMD) heterostructures can host novel correlated quantum phenomena due to the interplay of narrow moire flat bands and strong, long-range Coulomb interactions1–9. However, microscopic knowledge of the atomically reconstructed moire superlattice and resulting flat bands is still lacking, which is critical for fundamental understanding and control of the correlated moire phenomena. Here we quantitatively study the moire flat bands in three-dimensional (3D) reconstructed WSe2/WS2 moire superlattices by comparing scanning tunnelling spectroscopy (STS) of high-quality exfoliated TMD heterostructure devices with ab initio simulations of TMD moire superlattices. A strong 3D buckling reconstruction accompanied by large in-plane strain redistribution is identified in our WSe2/WS2 moire heterostructures. STS imaging demonstrates that this results in a remarkably narrow and highly localized K-point moire flat band at the valence band edge of the heterostructure. A series of moire flat bands are observed at different energies that exhibit varying degrees of localization. Our observations contradict previous simplified theoretical models but agree quantitatively with ab initio simulations that fully capture the 3D structural reconstruction. Our results reveal that the strain redistribution and 3D buckling in TMD heterostructures dominate the effective moire potential and the corresponding moire flat bands at the Brillouin zone K points. Scanning tunnelling spectroscopy and ab initio simulations reveal buckling reconstruction and in-plane strain redistribution in WSe2/WS2 moire heterostructures.

Graphene nanoribbons (GNRs) with widths of a few nanometres are promising candidates for future nano-electronic applications due to their structurally tunable bandgaps, ultrahigh carrier mobilities, and exceptional stability. However, the direct growth of micrometre-long GNRs on insulating substrates, which is essential for the fabrication of nano-electronic devices, remains an immense challenge. Here, we report the epitaxial growth of GNRs on an insulating hexagonal boron nitride (h-BN) substrate through nanoparticle-catalysed chemical vapor deposition (CVD). Ultra-narrow GNRs with lengths of up to 10 {\mu}m are synthesized. Remarkably, the as-grown GNRs are crystallographically aligned with the h-BN substrate, forming one-dimensional (1D) moir\'e superlattices. Scanning tunnelling microscopy reveals an average width of 2 nm and a typical bandgap of ~1 eV for similar GNRs grown on conducting graphite substrates. Fully atomistic computational simulations support the experimental results and reveal a competition between the formation of GNRs and carbon nanotubes (CNTs) during the nucleation stage, and van der Waals sliding of the GNRs on the h-BN substrate throughout the growth stage. Our study provides a scalable, single-step method for growing micrometre-long narrow GNRs on insulating substrates, thus opening a route to explore the performance of high-quality GNR devices and the fundamental physics of 1D moir\'e superlattices.

Detection of local strain at the nanometer scale with high sensitivity remains challenging. Here we report near-field infrared nano-imaging of local strains in bilayer graphene by probing strain-induced shifts of phonon frequency. As a non-polar crystal, intrinsic bilayer graphene possesses little infrared response at its transverse optical phonon frequency. The reported optical detection of local strain is enabled by applying a vertical electrical field that breaks the symmetry of the two graphene layers and introduces finite electrical dipole moment to graphene phonon. The activated phonon further interacts with continuum electronic transitions, and generates a strong Fano resonance. The resulted Fano resonance features a very sharp near-field infrared scattering peak, which leads to an extraordinary sensitivity of ∼ 0.002% for the strain detection. Our results demonstrate the first nano-scale near-field Fano resonance, provide a new way to probe local strains with high sensitivity in non-polar crystals, and open exciting possibilities for studying strain-induced rich phenomena.

Moiré superlattices in transition metal dichalcogenide (TMD) heterostructures can host novel correlated quantum phenomena due to the interplay of narrow moiré flat bands and strong, long-range Coulomb interactions

The evaluation for competitiveness of product is a prerequisite for product decisions, so it has an important practical significance to evaluate the competitiveness of product. This paper applies Analytic Hierarchy Process to establish the evaluation index system for competitiveness of network product, and constructs a mathematical model to evaluate the competitiveness by multi-level fuzzy evaluation method, then through the analysis of five online banking proves that the effectiveness and practicability of this evaluation method.

Regional innovation capability is the core factor for regional competition, so it has important practical significance to evaluate regional innovation capability. This paper applies analytic hierarchy process to establish the evaluation index system of regional innovation capability, and constructs a mathematical model by using grey relation projection method, and through analyzing the data of the 2006 covers Chinapsilas eight major regions proves that the effectiveness and practicability of this evaluation method.