Moiré is More: Access to New Properties of Two-Dimensional Layered Materials

Abstract

Expanding the properties of 2D materials and studying strong correlated systems is the focus of many researchers, for which the formation of moiré superlattices can provide access. With periodic moiré patterns, moiré superlattices can induce structural altering and band transformations, resulting in new phenomena including moiré phonons, moiré excitons, topological phase transition, unconventional superconductivity, or Mott insulation. Modulating moiré superlattices through altering twist angles can keep the intrinsic lattices and offer routes to new properties, which is more controllable for property tuning and beneficial for the development of novel physical models and theories. Moiré superlattices have recently become excellent platforms for studying new properties of two-dimensional (2D) layered materials. With periodic moiré patterns, moiré superlattices can induce structural altering and band transformations, resulting in new phenomena including moiré phonons, moiré excitons, topological phase transition, unconventional superconductivity, or Mott insulation. With specific moiré superlattices, bilayer or trilayer 2D materials (including heterostructures) can act as excellent models gathering interlayer interactions, intralayer features, band alignments, charge transport, and other effects (such as spin-orbit coupling and splitting) in a single system. This Review introduces the origin and the modulation of moiré superlattices and summarizes several series of new properties discovered in 2D layered materials. We believe that moiré superlattices mean new access to more structures, more properties, more physics, and more opportunities for both fundamental studies and applications of 2D materials. Moiré superlattices have recently become excellent platforms for studying new properties of two-dimensional (2D) layered materials. With periodic moiré patterns, moiré superlattices can induce structural altering and band transformations, resulting in new phenomena including moiré phonons, moiré excitons, topological phase transition, unconventional superconductivity, or Mott insulation. With specific moiré superlattices, bilayer or trilayer 2D materials (including heterostructures) can act as excellent models gathering interlayer interactions, intralayer features, band alignments, charge transport, and other effects (such as spin-orbit coupling and splitting) in a single system. This Review introduces the origin and the modulation of moiré superlattices and summarizes several series of new properties discovered in 2D layered materials. We believe that moiré superlattices mean new access to more structures, more properties, more physics, and more opportunities for both fundamental studies and applications of 2D materials. Since the successful fabrication of monolayer graphene in 2004, a variety of two-dimensional (2D) layered materials have been obtained and widely used in many fields including electronics, optoelectronics, energy storage, and catalysis.1Zeng M. Xiao Y. Liu J. Yang K. Fu L. Exploring two-dimensional materials toward the next-generation circuits: from monomer design to assembly control.Chem. Rev. 2018; 118: 6236-6296Crossref PubMed Scopus (120) Google Scholar, 2Novoselov K.S. Geim A.K. Morozov S.V. Jiang D. Zhang Y. Dubonos S.V. Grigorieva I.V. Firsov A.A. Electric field effect in atomically thin carbon films.Science. 2004; 306: 666-669Crossref PubMed Scopus (41694) Google Scholar, 3Liu J. Cao H. Jiang B. Xue Y. Fu L. Newborn 2D materials for flexible energy conversion and storage.Sci. 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Compared with other strategies, modulating moiré superlattices of 2D materials and heterostructures indicates the external alteration of each layer rather than the uncontrollable heteroatoms or defects, which tends to keep most of the intrinsic features and induce new properties. This makes it easier to explore more comprehensible and convinced explanations for these phenomena without the interference of structural defects. For homogeneous materials, moiré superlattices are mainly affected by the twist angle, while for heterostructures moiré superlattices highly rely on the twist angle as well as small lattice mismatch. Altering the twist angle can provide a powerful way for the modulation of lattice structures, band structures, and topological properties, and therefore can expand the properties or even create new physics of 2D materials. 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This paper reviews the innovative access to new properties of 2D layered materials induced by moiré superlattices. Starting with the origin of moiré superlattices, we present the new properties of few-layered graphene, graphene/hexagonal boron nitride (hBN) heterostructures, TMDs, TMD heterostructures, and other material with moiré superlattices. We then introduce how moiré patterns are formed and how to modulate the twist angles. Finally, we summarize the importance of moiré superlattices and demonstrate several challenges existing in the field. We expect that moiré superlattices should provide numerous opportunities to fundamental research and enable 2D materials to exhibit innovative properties and expand the applications. As atomically thin crystals assemble with one another, lattice mismatch and rotation between the layers can lead to different moiré superlattices, which are relevant to twist angles. The angle acts as a pivotal part in the properties of 2D layered materials, especially for van der Waals heterostructures. Recently great breakthroughs have been made in this field, and here we summarize the novel properties of various 2D materials and corresponding heterostructures with moiré patterns. Graphene has become a very flexible platform for engineering novel electronic and optoelectronic properties. Apart from combining graphene with other crystals to construct heterostructures, tuning the rotation angles between layers can also induce new properties and applications. When the layers are rotated to different angles, the periodicity of moiré superlattices will change accordingly, which has a great impact on the electronic structure and interlayer coupling of graphene. For the twisted bilayer graphene (TBG) with small twist angle (no larger than 5°), the interlayer coupling is strong and the Dirac band structure is sensitive to the angles.25Shallcross S. Sharma S. 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Early in 2011, Bistritzer and Macdonald established a low-energy continuum model Hamiltonian to study the moiré bands in bilayer graphene.26Bistritzer R. MacDonald A.H. Moiré bands in twisted double-layer graphene.Proc. Natl. Acad. Sci. U S A. 2011; 108: 12233-12237Crossref PubMed Scopus (0) Google Scholar They found that the velocity at the Dirac point is connected with the twist angle (θ), and when θ is close to 1.05° the Fermi velocity is near zero and the moiré band is flat—that is, the theoretically calculated magic angle is the angle at which the Fermi velocity at Dirac points becomes zero, where the electrons move slowly and are localized in the superlattice, resulting in strong correlation.27Kim K. DaSilva A. Huang S. Fallahazad B. Larentis S. Taniguchi T. Watanabe K. LeRoy B.J. MacDonald A.H. Tutuc E. Tunable moiré bands and strong correlations in small-twist-angle bilayer graphene.Proc. Natl. Acad. Sci. U S A. 2017; 114: 3364-3369Crossref PubMed Scopus (0) Google Scholar As shown in Figure 1B,17Cao Y. Fatemi V. Demir A. Fang S. Tomarken S.L. Luo J.Y. Sanchez-Yamagishi J.D. Watanabe K. Taniguchi T. Kaxiras E. et al.Correlated insulator behaviour at half-filling in magic-angle graphene superlattices.Nature. 2018; 556: 80-84Crossref PubMed Scopus (699) Google Scholar two kinds of single-layer graphene Dirac cones are rotated around the Γ point in the Brillouin zone by the twist angle θ. In consideration of the reciprocal lattice of the moiré superlattice, the differences between K and K′ wavevectors cause the mini-Brillouin zone. Besides, Dirac cones near the K or K′ valley partly overlap through interlayer hybridization. As a consequence, such hybridization helps open the energy gap and renormalize the Fermi velocity at Dirac points. To explore temperature dependency, Cao et al. studied the low-temperature conductance of TBG with moiré patterns (θ ≈ 1.08°) as a function of carrier density n (Figure 1C). They discovered a new half-filling insulating state (four electrons for per moiré unit cell), which did not exist in normal graphene. Based on the curves of the temperature-dependent conductance of the corresponding device (Figure 1E), it could be concluded that the superconducting transition temperature is 1.7 K. In addition to temperature, magnetic fields also have an influence on the conductance of half-filling states (Figure 1F). Therefore, unconventional superconducting in TBG superlattice is likely to be linked with the Mott-like state.17Cao Y. Fatemi V. Demir A. Fang S. Tomarken S.L. Luo J.Y. Sanchez-Yamagishi J.D. Watanabe K. Taniguchi T. 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