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 between different moiré exciton phases and their impact on optical properties of the twisted MoSe$_2$/WSe$_2$ heterostructure. At angles smaller than 2$^{\circ}$ we find flat, moiré trapped states for inter- and intralayer excitons. This moiré exciton phase drastically changes into completely delocalized states already at 3$^{\circ}$. We predict a linear and quadratic twist-angle dependence of excitonic resonances for the moiré-trapped and delocalized exciton phase, respectively. Our work provides microscopic insights opening the possibility to tailor moiré exciton phases in van der Waals superlattices.
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.
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…
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…
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 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…
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 …
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…
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 identify features in the angle-resolved photoemission spectra (ARPES) arising from the periodic pattern characteristic for graphene heterostructure with hexagonal boron nitride (hBN). For this, we model ARPES spectra and intensity maps for five microscopic models used previously to describe moire superlattice in graphene/hBN systems. We show that detailed analysis of these features can be used to pin down the microscopic mechanism of the interaction between graphene and hBN. We also analyze how the presence of a moire-periodic strain in graphene or scattering of photoemitted electrons off h…
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…
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 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…
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 …
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 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 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…
Graphene constitutes one of the key elements in many functional van der Waals heterostructures. However, it has negligible optical visibility due to its monolayer nature. Here we study the visibility of graphene in various van der Waals heterostructures and include the effects of the source spectrum, oblique incidence and the spectral sensitivity of the detector to obtain a realistic model. A visibility experiment is performed at different wavelengths, resulting in a very good agreement with our calculations. This allows us to reliably predict the conditions for better visibility of graphene i…
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…
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…
We report an experimental study of excitons in a double quantum well van der Waals heterostructure made of atomically thin layers of \Mo* and hexagonal boron nitride (hBN). The emission of neutral and charged excitons is controlled by gate voltage, temperature, and both the helicity and the power of optical excitation.
Indirect excitons (IXs) in van der Waals transition-metal dichalcogenide (TMD) heterostructures are characterized by a high binding energy making them stable at room temperature and giving the opportunity for exploring fundamental phenomena in excitonic systems and developing excitonic devices operational at high temperatures. We present the observation of IXs at room temperature in van der Waals TMD heterostructures based on monolayers of MoS$_2$ separated by atomically thin hexagonal boron nitride. The IXs realized in the TMD heterostructure have lifetimes orders of magnitude longer than lif…
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…
Moire superlattices in van der Waals (vdW) heterostructures could trap strongly bonded and long lived interlayer excitons. Assumed to be localized, these moire excitons could form ordered quantum dot arrays, paving the way for novel optoelectronic and quantum information applications. Here we perform first principles simulations to shed light on moire excitons in twisted MoS2/WS2 heterostructures. We provide the direct evidence of localized interlayer moire excitons in vdW heterostructures. The moire potentials are mapped out based on spatial modulations of energy gaps. Nearly flat valence ban…
Van der Waals heterostructures built by vertically stacked transition metal dichalcogenides (TMDs) exhibit a rich energy landscape including interlayer and intervalley excitons. Recent experiments demonstrated an ultrafast charge transfer in TMD heterostructures. However, the nature of the charge transfer process has remained elusive. Based on a microscopic and material-realistic exciton theory, we reveal that phonon-mediated scattering via strongly hybridized intervalley excitons governs the charge transfer process that occurs on a sub-100fs timescale. We track the time-, momentum-, and energ…
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…
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…
We develop a theory for interlayer tunneling in van der Waals heterostructures driven under a strong electromagnetic field, using graphene/{\it h}-BN/graphene as a paradigmatic example. Our theory predicts that strong anti-resonances appear at bias voltage values equal to an integer multiple of the light frequency. These features are found to originate from photon-assisted resonant tunneling transitions between Floquet sidebands of different graphene layers, and are unique to two-band systems due to the interplay of both intraband and interband tunneling transitions. Our results point to the p…
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.
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））
In van der Waals heterostructures, electronic bands of two-dimensional (2D) materials, their nontrivial topology, and electron-electron interactions can be dramatically changed by a moire pattern induced by twist angles between different layers. Such process is referred to as twistronics, where the tuning of twist angle can be realized through mechanical manipulation of 2D materials. Here we demonstrate an experimental technique that can achieve in situ dynamical rotation and manipulation of 2D materials in van der Waals heterostructures. Using this technique we fabricated heterostructures whe…
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…
Two-dimensional (2D) van der Waals heterostructures serve as a promising platform to exploit various physical phenomena in a diverse range of novel spintronic device applications. The efficient spin injection is the prerequisite for these devices. The recent discovery of magnetic 2D materials leads to the possibility of fully 2D van der Waals spintronics devices by implementing spin injection through magnetic proximity effect (MPE). Here, we report the investigation of magnetic proximity effect in 2D CrBr3/graphene van der Waals heterostructures, which is probed by Zeeman spin Hall effect thro…
Investigating thermal transport in van der Waals heterostructure is of scientific interest and practical importance for their applications in a broad range. In this work, thermal conductivity of one-dimensional heterostructure consisting of carbon and boron nitride nanotubes is systematically investigated via molecular dynamics simulations. Thermal conductivity is found to have strong dependences on temperature, length and diameter. In addition, the axial strain and intensity of van der Waals interaction are demonstrated to be able to modulate thermal conductivity up to about 43% and 37%, resp…
