We report deterministic control over moiré superlattice interference pattern in twisted bilayer graphene by implementing designable device-level heterostrain with process-induced strain engineering, a widely used technique in industrial silicon nanofabrication processes. By depositing stressed thin films onto our twisted bilayer graphene samples, heterostrain magnitude and strain directionality can be controlled by stressor film force (film stress x film thickness) and patterned stressor geometry, respectively. We examine strain and moiré interference with Raman spectroscopy through in-plane and moiré-activated phonon mode shifts. Results support systematic C$_{3}$ rotational symmetry breaking and tunable periodicity in moiré superlattices under the application of uniaxial or biaxial heterostrain. Experimental results are validated by molecular statics simulations and density functional theory based first principles calculations. This provides a method to not only tune moiré interference without additional twisting, but also allows for a systematic pathway to explore different van der Waals based moiré superlattice symmetries by deterministic design.
The discovery of unconventional ferroelectric behavior in twisted bilayers has prompted the consideration of moiré heterostructures as polar materials. However, misconceptions about the nature and origin of the observed ferroelectricity indicate that a better theoretical understanding of the polar properties of moiré heterostructures is needed. In this paper, it is proposed, and verified with first-principles calculations, that all moiré heterostructures exhibit an out-of-plane moiré polar domain (MPD) structure. In transition metal dichalcogenide bilayers, an interlayer charge transfer occurs…
We consider the role of deformations in graphene heterostructures with hexagonal crystals (including strain, wrinkles and dislocations) on the geometrical properties of moire patterns characteristic for a pair of two incommensurate misaligned isostructural crystals. By, employing a phenomenological theory to describe generic moire perturbation in van der Waals heterostructures of graphene and hexagonal crystals we investigate the electronic properties of such heterostructure.
Van der Waals heterostructures of graphene and hexagonal boron nitride feature a moiré superlattice for graphene's Dirac electrons. Here, we review the effects generated by this superlattice, including a specific miniband structure featuring gaps and secondary Dirac points, and a fractal spectrum of magnetic minibands known as Hofstadter's butterfly.
Stacking monolayers of transition metal dichalcogenides into a heterostructure with a finite twist-angle gives rise to artificial moiré superlattices with a tunable periodicity. As a consequence, excitons experience a periodic potential, which can be exploited to tailor optoelectronic properties of these materials. While recent experimental studies have confirmed twist-angle dependent optical spectra, the microscopic origin of moiré exciton resonances has not been fully clarified yet. Here, we combine first principle calculations with the excitonic density matrix formalism to study transitions…
Moiré heterostructures are rapidly emerging as a tunable platform to study correlated electronic phenomena. Discovery of exotic quantum phases in moiré systems requires novel probes of charge and spin order. Unlike detection schemes which average over several moiré cells, local sensors can provide richer information with greater sensitivity. We study a WSe$_2$/MoSe$_2$/WSe$_2$ heterotrilayer which hosts excitons and electrons in distinct moiré lattices, and show that localized dipolar excitons are sensitive proximity charge sensors, uncovering numerous correlated electronic states at fractiona…
Moiré superlattices provide a powerful tool to engineer novel quantum phenomena in two-dimensional (2D) heterostructures, where the interactions between the atomically thin layers qualitatively change the electronic band structure of the superlattice. For example, mini-Dirac points, tunable Mott insulator states, and the Hofstadter butterfly can emerge in different types of graphene/boron nitride moiré superlattices, while correlated insulating states and superconductivity have been reported in twisted bilayer graphene moiré superlattices. In addition to their dramatic effects on the single pa…
Formation of moiré superlattices is common in Van der Waals heterostructures as a result of the mismatch between lattice constants and misalignment of crystallographic directions of the constituent two-dimensional crystals. We discuss theoretically electron transport in a Van der Waals tunnelling transistor in which one of the electrodes is made of two crystals forming a moiré superlattice at their interface. By investigating structures containing either the aligned graphene/hexagonal boron nitride heterostructure or twisted bilayer graphene, we show that negative differential resistance is po…
Moiré superlattices provide a powerful way to engineer properties of electrons and excitons in two-dimensional van der Waals heterostructures. The moiré effect can be especially strong for interlayer excitons, where electrons and holes reside in different layers and can be addressed separately. In particular, it was recently proposed that the moiré superlattice potential not only localizes interlayer exciton states at different superlattice positions, but also hosts an emerging moiré quasi-angular momentum (QAM) that periodically switches the optical selection rules for interlayer excitons at …
Moiré superlattices of van der Waals heterostructures provide a powerful new way to engineer the electronic structures of two-dimensional (2D) materials. Many novel quantum phenomena have emerged in different moiré heterostructures, such as correlated insulators, superconductors, and Chern insulators in graphene systems and moiré excitons in transition metal dichalcogenide (TMDC) systems. Twisted phosphorene offers another attractive system to explore moiré physics because phosphorene features an anisotropic rectangular lattice, different from the isotropic hexagonal lattice in graphene and TM…
The emergence of a topological superconducting state in van der Waals heterostructures provides a new platform for exploring novel strategies to control topological superconductors. In particular, impurities in van der Waals heterostructures, generically featuring a moire pattern, can potentially lead to the unique interplay between atomic and moire length scales, a feature absent in generic topological superconductors. Here we address the impact of non-magnetic impurities on a topological moire superconductor, both in the weak and strong regime, considering both periodic arrays and single imp…
In heterostructures consisting of atomically thin crystals layered on top of one another, lattice mismatch or rotation between the layers results in long-wavelength moiré superlattices. These moiré patterns can drive significant band structure reconstruction of the composite material, leading to a wide range of emergent phenomena including superconductivity, magnetism, fractional Chern insulating states, and moiré excitons. Here, we investigate monolayer graphene encapsulated between two crystals of boron nitride (BN), where the rotational alignment between all three components can be varied. …
We investigate the effect of sliding motion of layers in Moiré heterostructures on the electronic state. We show that the sliding Moiré heterostructure can generate nontrivial topology characterized by the first and second Chern number in the high dimensional manifold spanned by the physical dimensions and synthetic dimensions associated with the sliding displacement. The nontrivial topology implies a topological charge pumping caused by the sliding motion. We demonstrate the nontrivial topology and charge pumping explicitly in a one dimensional bi-chain model and the small-angle twisted bilay…
In van der Waals (vdW) heterostructures formed by stacking two monolayer semiconductors, lattice mismatch or rotational misalignment introduces an in-plane moiré superlattice. While it is widely recognized that a moiré superlattice can modulate the electronic band structure and lead to novel transport properties including unconventional superconductivity and insulating behavior driven by correlations, its influence on optical properties has not been investigated experimentally. We present spectroscopic evidence that interlayer excitons are confined by the moiré potential in a high-quality MoSe…
We present a phenomenological theory of the low energy moiré minibands of Dirac electrons in graphene placed on an almost commensurate hexagonal underlay with a unit cell pproximately three times larger than that of graphene.A slight incommensurability results in a periodically modulated intervalley scattering for electrons in graphene. In contrast to the perfectly commensurate Kekulé distortion of graphene, such supperlattice perturbation leaves the zero energy Dirac cones intact, but is able to open a band gap at the edge of the first moiré subbband, asymmetrically in the conduction and vale…
We reexamine the electronic structure of graphene on SiC substrate by angle-resolved photoemission spectroscopy. We directly observed multiply cloning of Dirac cone, in addition to ones previously attributed to reconstruction. The locations, relative distances and anisotropy of Dirac cone replicas fully agree with the moiré pattern of graphene-SiC heterostructure. Our results provide a straightforward example of moiré potential modulation in engineering electronic structure with Dirac fermions.
The incommensurate stacking of multi-layered two-dimensional materials is a challenging problem from a theoretical perspective and an intriguing avenue for manipulating their physical properties. Here we present a multi-scale model to obtain the mechanical relaxation pattern of twisted trilayer van der Waals (vdW) heterostructures with two independent twist angles, a generally incommensurate system without a supercell description. We adopt the configuration space as a natural description of such incommensurate layered materials, based on the local environment of atomic positions, bypassing the…
Spatially periodic structures with a long range period, referred to as moiré pattern, can be obtained in van der Waals bilayers in the presence of a small stacking angle or of lattice mismatch between the monolayers. Theoretical predictions suggest that the resulting spatially periodic variation of the band structure modifies the optical properties of both intra and interlayer excitons of transition metal dichalcogenides heterostructures. Here, we report on the impact of the moiré pattern formed in a MoSe$_2$/MoS$_2$ heterobilayer encapsulated in hexagonal boron nitride. The periodic in-plane …
The properties of van der Waals (vdW) heterostructures are drastically altered by a tunable moiré superlattice arising from periodic variations of atomic alignment between the layers. Exciton diffusion represents an important channel of energy transport in semiconducting transition metal dichalcogenides (TMDs). While early studies performed on TMD heterobilayers have suggested that carriers and excitons exhibit long diffusion lengths, a rich variety of scenarios can exist. In a moiré crystal with a large supercell size and deep potential, interlayer excitons may be completely localized. As the…
Ideal Topological Flat Bands in Two-dimensional Moiré Heterostructures with Type-II Band Alignment
The Pennsylvania State University（宾夕法尼亚州立大学）；Northeastern University（东北大学）；University of Washington（华盛顿大学）；Princeton University（普林斯顿大学）；Donostia International Physics Center（圣塞巴斯蒂安国际物理中心）；IKERBASQUE, Basque Foundation for Science（伊克拉巴斯基克，巴斯克科学基金会）
Controlling matter-light interactions with cavities is of fundamental importance in modern science and technology. It is exemplified in the strong-coupling regime, where matter-light hybrid modes form, with properties controllable via the photon component on the optical-wavelength scale. In contrast, matter excitations on the nanometer scale are harder to access. In two-dimensional van der Waals heterostructures, a tunable moiré lattice potential for electronic excitations may form, enabling correlated electron gases in lattice potentials. Excitons confined in moiré lattices have also been rep…
The specific rotational alignment of two-dimensional lattices results in a moiré superlattice with a larger period than the original lattices and allows one to engineer the electronic band structure of such materials. So far, transport signatures of such superlattices have been reported for graphene/hBN and graphene/graphene systems. Here we report moiré superlattices in fully hBN encapsulated graphene with both the top and the bottom hBN aligned to the graphene. In the graphene, two different moiré superlattices form with the top and the bottom hBN, respectively. The overlay of the two superl…
The superlattice of alternating graphene/h-BN few-layered heterostructures is found to exhibit strong dependence on the parity of the number of layers within the stack. Odd-parity systems show a unique flamingo-like pattern, whereas their even-parity counterparts exhibit regular hexagonal or rectangular superlattices. When the alternating stack consists of seven layers or more, the flamingo pattern becomes favorable, regardless of parity. Notably, the out-of-plane corrugation of the system strongly depends on the shape of the superstructure resulting in significant parity dependence of its mec…
We have studied the electronic excitation spectrum in periodically rippled graphene on Ru(0001) and flat, commensurate graphene on Ni(111) by means of high-resolution electron energy loss spectroscopy and a combination of density functional theory and tight-binding approaches. We show that the periodic moiré superlattice originated by the lattice mismatch in graphene/Ru(0001) induces the emergence of an extra mode, which is not present in graphene/Ni(111). Contrary to the ordinary intra-band plasmon of doped graphene, the extra mode is robust in charge-neutral graphene/metal contacts, having i…
Twisted atomically thin semiconductors are characterized by moiré excitons. Their optical signatures and selection rules are well understood. However, their hybridization with photons in the strong coupling regime for heterostructures integrated in an optical cavity has not been in the focus of research yet. Here, we combine an excitonic density matrix formalism with a Hopfield approach to provide microscopic insights into moiré exciton polaritons. In particular, we show that exciton-light coupling, polariton energy, and even the number of polariton branches can be controlled via the twist ang…
Resonant absorption and linear photovoltaic effect in ferroelectric moiré heterostructures
Moscow Center for Advanced Studies（莫斯科高级研究中心）；Kotelnikov Institute of Radio-engineering and Electronics of the RAS（俄罗斯科学院科特利尼科夫无线电工程与电子研究所）；HSE University（国立高等经济学院）；Institute of Physics of DFRS of the RAS（俄罗斯科学院达吉斯坦共和国科学中心物理研究所）
Vertical stacking of atomically thin materials offers a large platform for realizing novel properties enabled by proximity effects and moiré patterns. Here we focus on mechanically assembled heterostructures of graphene and ReS$_2$, a van der Waals layered semiconductor. Using scanning tunneling microscopy and spectroscopy (STM/STS) we image the sharp edge between the two materials as well as areas of overlap. Locally resolved topographic images revealed the presence of a striped superpattern originating in the interlayer interactions between graphene's hexagonal structure and the triclinic, l…
Periodicity of long wavelength moiré patterns is very often destroyed by the inhomogeneous strain introduced in fabrications of van der Waals layered structures. We present a framework to describe massive Dirac fermions in such distorted moiré pattern of transition metal dichalcogenides homobilayers, accounting for the dynamics of layer pseudospin. In decoupled bilayers, we show two causes of in-plane layer pseudospin precession: By the coupling of layer antisymmetric strain to valley magnetic moment; and by the Aharonov-Bohm effect in the SU(2) gauge potential for the case of R-type bilayer u…
In bilayers of semiconducting transition metal dichalcogenides, the twist angle between layers can be used to introduce a highly regular periodic potential modulation on a length scale that is large compared to the unit cell. In such structures, correlated states can emerge, in which excitons in the heterostructure are strongly localized to the potential minima due to exciton-exciton interactions. We explore the transition between Mott and extended exciton phases in terms of a moiré-Bose-Hubbard Hamiltonian. Hopping and on-site interaction parameters are obtained from a Wannier representation …
Most studies on moiré superlattices formed from a stack of h-BN and graphene have focused on single layer graphene; graphene with multiple layers is less understood. Here, we show that a moiré superlattice of multilayer graphene shows new features arising from the anisotropic Fermi surface affected by the superlattice structure. The moiré superlattice of a h-BN/AB-stacked tetralayer graphene heterostructure exhibited resistivity peaks showing a complicated dependence on the perpendicular electric field. The peaks were not due to secondary Dirac cones forming, but rather opening of the energy g…
Twisting moiré heterostructures to the flatband regime allows for the formation of strongly correlated quantum states, since the dramatic reduction of the bandwidth can cause the residual electronic interactions to set the principal energy scale. An effective description for such correlated moiré heterostructures, derived in the strong-coupling limit at integer filling, generically leads to spin-valley Heisenberg models. Here we explore the emergence and stability of spin liquid behavior in an SU(2)$^{\mathrm{spin}}\otimes$SU(2)$^{\mathrm{valley}}$ Heisenberg model upon inclusion of Hund's-ind…
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 interactions1-5. However, microscopic knowledge of the atomically-reconstructed moiré superlattice and resulting flat bands is still lacking, which is critical for fundamental understanding and control of the correlated moiré phenomena. Here we quantitatively study the moiré flat bands in three-dimensional (3D) reconstructed WSe2/WS2 moiré superlattices by comparing scanning tunneling spectroscop…
We report the epitaxial growth of PdTe$_2$ ultrathin films on topological insulator Bi$_2$Se$_3$. A prominent Moiré pattern was observed in STM measurements. The Moiré periodicity increases as film thickness decreases, indicating a lattice expansion of epitaxial PdTe$_2$ thin films with lower thicknesses. In addition, our simulations based on Moiré Metrology reveal uniaxial lattice strains at the edge of PdTe$_2$ domains, and anisotropic strain distributions throughout the Moiré supercell with a net change in lattice strain up to ~2.9%. Our DFT calculations show that this strain effect leads t…
Light-matter interactions in layered materials and heterostructures: from moiré physics and magneto-optical effects to ultrafast dynamics and hybrid meta-photonics
In long-wavelength moiré superlattices of stacked transition metal dichalcogenides (TMDs), structural reconstruction ubiquitously occurs, which has reported to impact significantly their electronic properties. However, complete microscopic understandings of the interplay between the lattice reconstruction and alteration of electronic properties, and their further response to external perturbations in the reconstructed TMDs moiré superlattice are still lacking. Here, using scanning tunneling microscopy (STM) and scanning tunneling spectroscopy (STS) combined with first-principles calculation, w…
Driven-dissipative superconductivity in moiré heterostructure without attraction
Joint Quantum Institute, University of Maryland（马里兰大学联合量子研究所）；ICFO-Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology（巴塞罗那科技大学光子科学研究所）；Institute of Quantum Electronics, ETH Zürich（苏黎世联邦理工学院量子电子学研究所）；Institute for Theoretical Physics, University of Cologne（科隆大学理论物理研究所）
Twist and strain identification in moiré heterostructures
Wuhan University（武汉大学）；Key Laboratory of Artificial Micro- and Nano-structures of Ministry of Education（教育部人工微结构和介观物理重点实验室）；School of Physics and Technology, Wuhan University（武汉大学物理科学与技术学院）；IMDEA Nanoscience（IMDEA纳米科学研究所）；Weizmann Institute of Science（魏茨曼科学研究所）；Department of Condensed Matter Physics, Weizmann Institute of Science（魏茨曼科学研究所凝聚态物理系）；University of Washington（华盛顿大学）；Department of Physics, University of Washington（华盛顿大学物理系）；Hainan University（海南大学）；Center for Theoretical Physics, Hainan University（海南大学理论物理中心）；School of Physics and Optoelectronic Engineering, Hainan University（海南大学物理与电子工程学院）；Donostia International Physics Center（圣塞巴斯蒂安国际物理中心）
Moiré structures in van der Waals heterostructures lead to emergent phenomena including superconductivity in twisted bilayer graphene and optically accessible strongly-correlated electron states in transition metal dichalcogenide heterobilayers. Dual periodicity moiré structures (DPMS) formed in layered structures with more than two layers have been shown to lead to ferromagnetism and multiple secondary Dirac points in TBG. Whilst in principle it is possible to obtain DPMS in bilayers there has not been clear experimental evidence of this yet. In this paper we present signatures of DPMS in a t…
The emerging field of twistronics, which harnesses the twist angle between two-dimensional materials, represents a promising route for the design of quantum materials, as the twist-angle-induced superlattices offer means to control topology and strong correlations. At the small twist limit, and particularly under strain, as atomic relaxation prevails, the emergent moiré superlattice encodes elusive insights into the local interlayer interaction. Here we introduce moiré metrology as a combined experiment-theory framework to probe the stacking energy landscape of bilayer structures at the 0.1 me…
Commensuration torques in double-moiré twisted trilayer hexagonal boron nitride and graphene heterostructures
University of Seoul（首尔大学）；Sungkyunkwan University（成均馆大学）；Catalan Institute of Nanoscience and Nanotechnology (ICN2), CSIC and BIST（加泰罗尼亚纳米科学与技术研究所（ICN2，西班牙高等科学研究委员会和巴塞罗那独立科学研究所））
