Moiré metrology of energy landscapes in van der Waals heterostructures
Dorri Halbertal, Nathan R. Finney, Sai S. Sunku, Alexander Kerelsky, Carmen Rubio-Verdú, Sara Shabani, Lede Xian, Stephen Carr, Shaowen Chen, Charles Zhang, Lei… 展开作者
Dorri Halbertal, Nathan R. Finney, Sai S. Sunku, Alexander Kerelsky, Carmen Rubio-Verdú, Sara Shabani, Lede Xian, Stephen Carr, Shaowen Chen, Charles Zhang, Lei Wang, Derick Gonzalez-Acevedo, Alexander S. McLeod, Daniel Rhodes, Kenji Watanabe, Takashi Taniguchi, Efthimios Kaxiras, Cory R. Dean, James C. Hone, Abhay N. Pasupathy, Dante M. Kennes, Angel Rubio, D. N. Basov
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 meV/atom scale, outperforming the gold-standard of quantum chemistry. Through studying the shapes of moiré domains with numerous nano-imaging techniques, and correlating with multi-scale modelling, we assess and refine first-principle models for the interlayer interaction. We document the prowess of moiré metrology for three representative twisted systems: bilayer graphene, double bilayer graphene and H-stacked $MoSe_2/WSe_2$. Moiré metrology establishes sought after experimental benchmarks for interlayer interaction, thus enabling accurate modelling of twisted multilayers.
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.
Different atomistic registry between the layers forming the inner and outer nanotubes can form one-dimensional (1D) van der Waals (vdW) moiré superlattices. Unlike the two-dimensional (2D) vdW moiré superlattices, effects of 1D vdW moiré superlattices on electronic and optical properties in 1D moiré superlattices are not well understood, and they are often neglected. In this Perspective, we summarize new experimental observations and theoretical perspectives related to interlayer interactions in double-walled carbon nanotubes (DWNTs), a representative 1D vdW moiré system. Our discussion will f…
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.
The spatial dependence of the van der Waals (vdW) energy between graphene and hexagonal boron-nitride (h-BN) is investigated using atomistic simulations. The van der Waals energy between graphene and h-BN shows a hexagonal superlattice structure identical to the observed Moiré pattern in the local density of states (LDOS) which depends on the lattice mismatch and misorientation angle between graphene and h-BN. Our results provide atomistic features of the weak van der Waals interaction between graphene and BN which are in agreement with experiment and provide an analytical expression for the s…
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…
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…
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…
We explore the skyrmion formation and control possibilities in 2D magnets from the ubiquitous moiré pattern in vdW heterostructures. Using the example of a ferromagnetic monolayer on an antiferromagnetic substrate, we demonstrate a new origin of skyrmions in the 2D magnets, from the lateral modulation of interlayer magnetic coupling by the locally different atomic registries in moiré. The moiré skyrmions are doubly degenerate with opposite topological charge, and trapped at an ordered array of sites with the moiré periodicity that can be dramatically tuned by strain and interlayer translation.…
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…
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…
We investigated experimentally the valley Zeeman splitting of excitonic peaks in the photoluminescence (PL) spectra of high-quality hBN/WS2/MoSe2/hBN heterostructures at near-zero twist angles under perpendicular magnetic fields up to 20 T. We identify two neutral exciton peaks in the PL spectra: the lower energy one exhibits a reduced g-factor relative to that of the higher energy peak, and much lower than the recently reported values for interlayer excitons in other van der Waals (vdW) heterostructures. We provide evidence that such a discernible g-factor stems from the spatial confinement o…
The optical and electronic properties of van der Waals (vdW) heterostructures depend strongly on the atomic stacking order of the constituent layers. This is exemplified by periodic variation of the local atomic registry, known as moire patterns, giving rise to superconductivity and ferromagnetism in twisted bilayer graphene and novel exciton states in transition metal dichalcogenides (TMD) heterobilayers. However, the presence of the nanometer-scale moire superlattices is typically deduced indirectly, because conventional imaging techniques, such as transmission electron microscopy (TEM), req…
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…
We investigate the magnetic proximity effect in van der Waals heterostructure formed by a monolayer semiconductor stacked on a 2D ferromagnet, where the lattice mismatch and twisting between the layers typically lead to the formation of moiré pattern. We find that the magnetic proximity effect arising from the spin dependent interlayer coupling depends sensitively on the interlayer atomic registry. Consequently, in the moiré pattern, the spatial variation of the atomic registry leads to a lateral modulation of magnetic proximity field. Such moiré modulated magnetic proximity effect manifests a…
Stacking-dependent interlayer interactions are important for understanding the structural and electronic properties in incommensurable two dimensional material assemblies where long-range moiré patterns arise due to small lattice constant mismatch or twist angles. Here, we study the stacking-dependent interlayer coupling energies between graphene (G) and hexagonal boron nitride (BN) homo- and hetero-structures using high-level random-phase approximation (RPA) ab initio calculations. Our results show that although total binding energies within LDA and RPA differ substantially between a factor o…
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…
Sliding and twisting van der Waals layers with respect to each other gives rise to moiré structures with emergent electronic properties. Electrons in these moiré structures feel weak potentials that are typically in the tens of millielectronvolt range when the moiré structures are smooth at the atomic scale. Here we report a facile technique to achieve deep, deterministic trapping potentials via strain-based moiré engineering in van der Waals bilayers. We use elasto-scanning tunneling microscopy to show that uniaxial strain drives a commensurate-incommensurate lattice transition in a multilaye…
Even if individual two-dimensional materials own various interesting and unexpected properties, the stacking of such layers leads to van der Waals solids which unite the characteristics of two dimensions with novel features originating from the interlayer interactions. In this topical review, we cover fabrication and characterization of van der Waals heterosructures with a focus on heterobilayers made of monolayers of semiconducting transition metal dichalcogenides. Experimental and theoretical techniques to investigate those heterobilayers are introduced. Most recent findings focusing on diff…
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…
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…
Moiré superlattices open an unprecedented opportunity for tailoring interactions between quantum particles and their coupling to electromagnetic fields. Strong superlattice potential generates moiré minibands of excitons -- bound pairs of electrons and holes that reside either in a single layer (intralayer excitons) or two separate layers (interlayer excitons). The twist-angle-controlled interlayer hybridization of carriers can also mix the two types of excitons to combine the strengths of both. Here, we report a direct observation of spatially mixed moiré excitons in angle-aligned WSe2/WS2 an…
Moiré superlattices formed in van der Waals bilayers have enabled the creation and manipulation of new quantum states, as is exemplified by the discovery of superconducting and correlated insulating states in twisted bilayer graphene near the magic angle. Twisted bilayer semiconductors may lead to tunable exciton lattices and topological states, yet signatures of moiré excitons have been reported only in closely angularly-aligned bilayers. Here we report tuning of moiré lattice in WS$_{2}$ /MoSe$_{2}$ bilayers over a wide range of twist angles, leading to the continuous tuning of moiré lattice…
Van der Waals (vdW) heterostructures formed by 2D atomic crystals provide a powerful approach towards designer condensed matter systems. Incommensurate heterobilayers with small twisting and/or lattice mismatch lead to the interesting concept of Moiré superlattice, where the atomic registry is locally indistinguishable from commensurate bilayers but has local-to-local variation over long range. Here we show that such Moiré superlattice can lead to periodic modulation of local topological order in vdW heterobilayers formed by two massive Dirac materials. By tuning the vdW heterojunction from no…
Quantum spin-liquid van der Waals magnets such as TaS$_2$, TaSe$_2$, and RuCl$_3$ provide a natural platform to explore new exotic phenomena associated with spinon physics, whose properties can be controlled by exchange proximity with ferromagnetic insulators such as CrBr$_3$. Here we put forward a twisted van der Waals heterostructure based on a quantum spin-liquid bilayer encapsulated between ferromagnetic insulators. We demonstrate the emergence of spinon flat bands and topological spinon states in such heterostructure, where the emergence of a topological gap is driven by the twist. We fur…
Moiré patterns are common in Van der Waals heterostructures and can be used to apply periodic potentials to elementary excitations. We show that the optical absorption spectrum of transition metal dichalcogenide bilayers is profoundly altered by long period moiré patterns that introduce twist-angle dependent satellite excitonic peaks. Topological exciton bands with non-zero Chern numbers that support chiral excitonic edge states can be engineered by combining three ingredients: i) the valley Berry phase induced by electron-hole exchange interactions, ii) the moiré potential, and iii) the valle…
Magnetic skyrmions in 2D chiral magnets are in general stabilized by a combination of Dzyaloshinskii-Moriya interaction and external magnetic field. Here, we show that skyrmions can also be stabilized in twisted moiré superlattices in the absence of an external magnetic field. Our setup consists of a 2D ferromagnetic layer twisted on top of an antiferromagnetic substrate. The coupling between the ferromagnetic layer and the substrate generates an effective alternating exchange field. We find a large region of skyrmion crystal phase when the length scales of the moiré periodicity and skyrmions …
Van der Waals layered materials, such as transition metal dichalcogenides (TMDs), are an exciting class of materials with weak interlayer bonding which enables one to create van der Waals heterostructures (vdWH). Recent work has shown that control of the twist angle between layers can have a dramatic effect on vdWH properties. For TMD vdWH, twist angle has been treated solely through the use of rigid-lattice moiré patterns. No atomic reconstruction, i.e. any rearrangement of atoms within the individual layers, has been reported experimentally to date. Here we demonstrate that vdWH of MoSe2/WSe…
We show that anisotropic energy of a 2D antiferromagnet is greatly enhanced via stacking on a magnetic substrate layer, arising from the sublattice-dependent interlayer magnetic interaction that defines an effective anisotropic energy. Interestingly, this effective energy couples strongly with the interlayer stacking order and the magnetic order of the substrate layer, providing unique mechanical and magnetic means to control the antiferromagnetic order. These two types of control methods affect distinctly the sublattice magnetization dynamics, with a change of the ratio of sublattice precessi…
We investigate the magnetic minibands of a heterostructure consisting of bilayer graphene (BLG) and hexagonal boron nitride (hBN) by numerically diagonalizing a two-band Hamiltonian that describes electrons in BLG in the presence of a moire potential. Due to inversion-symmetry breaking characteristic for the moire potential, the valley symmetry of the spectrum is broken, but despite this, the zero-energy Landau level in BLG survives, albeit with reduced degeneracy. In addition, we derive effective models for the low-energy features in the magnetic minibands and demonstrate the appearance of se…
Moiré superlattices can induce correlated-electronic phases in twisted van-der-Waals materials. Strongly correlated quantum phenomena emerge, such as superconductivity and the Mott-insulating state. However, moiré superlattices produced through artificial stacking can be quite inhomogeneous, which hampers the development of a clear correlation between the moiré period and the emerging electrical and optical properties. Here we demonstrate in twisted-bilayer transition-metal dichalcogenides that low-frequency Raman scattering can be utilized not only to detect atomic reconstruction, but also to…
Moiré superlattices from stacks of van der Waals materials offer an exciting arena in the fields of condensed matter physics and materials science. Typically, these moiré superlattices consist of materials with identical or similar structures, and the long moiré period arises from a small twist angle or lattice mismatch. In this article, we discuss that long moiré period appears in a new moiré system by stacking two dissimilar van der Waals layers with large lattice mismatch, resulting in couplings between moiré bands from remote valleys in the momentum space. In this system, the first layer i…
Atomically-thin layers of two-dimensional materials can be assembled in vertical stacks held together by relatively weak van der Waals forces, allowing for coupling between monolayer crystals with incommensurate lattices and arbitrary mutual rotation. A profound consequence of using these degrees of freedom is the emergence of an overarching periodicity in the local atomic registry of the constituent crystal structures, known as a moiré superlattice. Its presence in graphene/hexagonal boron nitride (hBN) structures led to the observation of electronic minibands, whereas its effect enhanced by …
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…
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 …
By atomistic modeling of moir{é} patterns of graphene on a substrate with a small lattice mismatch, we find qualitatively different strain distributions for small and large misorientation angles, corresponding to the commensurate-incommensurate transition recently observed in graphene on hexagonal BN. We find that the ratio of C-N and C-B interactions is the main parameter determining the different bond lengths in the center and edges of the moir{é} pattern. Agreement with experimental data is obtained only by assuming that the C-B interactions are at least twice weaker than the C-N interactio…
In moiré crystals formed by stacking van der Waals (vdW) materials, surprisingly diverse correlated electronic phases and optical properties can be realized by a subtle change in the twist angle. Here, we discover that phonon spectra are also renormalized in MoS$_2$ twisted bilayers, adding a new perspective to moiré physics. Over a range of small twist angles, the phonon spectra evolve rapidly due to ultra-strong coupling between different phonon modes and atomic reconstructions of the moiré pattern. We develop a new low-energy continuum model for phonons that overcomes the outstanding challe…
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…
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 …
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…
Layered two-dimensional materials exhibit rich transport and optical phenomena in twisted or lattice-incommensurate heterostructures with spatial variations of interlayer hybridization arising from moiré interference effects. Here, we report experimental and theoretical studies of excitons in twisted heterobilayers and heterotrilayers of transition metal dichalcogenides. Using MoSe$_2$-WSe$_2$ stacks as representative realizations of twisted van der Waals bilayer and trilayer heterostructures, we observe contrasting optical signatures and interpret them in the theoretical framework of interlay…
Moiré engineering has recently emerged as a capable approach to control quantum phenomena in condensed matter systems. In van der Waals heterostructures, moiré patterns can be formed by lattice misorientation between adjacent atomic layers, creating long range electronic order. To date, moiré engineering has been executed solely in stacked van der Waals multilayers. Herein, we describe our discovery of electronic moiré patterns in films of a prototypical magnetoresistive oxide La0.67Sr0.33MnO3 (LSMO) epitaxially grown on LaAlO3 (LAO) substrates. Using scanning probe nano-imaging, we observe mi…
Using bilayer CrI$_3$ as an example, we demonstrate that stacking domain walls in van der Waals magnets can host one dimensional (1D) magnon channels, which have lower energies than bulk magnons. Interestingly, some magnon channels are hidden in magnetically homogeneous background and can only be inferred with the knowledge of stacking domain walls. Compared to 1D magnons confined in magnetic domain walls, 1D magnons in stacking domain walls are more stable against external perturbations. We show that the relaxed moiré superlattices of small-angle twisted bilayer CrI$_3$ is a natural realizati…
