Twisted 2D bilayer materials are created by artificial stacking of two monolayer crystal networks of 2D materials with a desired twisting angle $θ$. The material forms a moiré superlattice due to the periodicity of both top and bottom layer crystal structure. The optical properties are modified by lattice reconstruction and phonon renormalization, which makes optical spectroscopy an ideal characterization tool to study novel physics phenomena. Here, we report a Raman investigation on a full period of the twisted bilayer (tB) WSe$_2$ moiré superlattice (\textit i.e. 0° $\leq θ\leq$ 60°). We observe that the intensity ratio of two Raman peaks, $B_{2g}$ and $E_{2g}/A_{1g}$ correlates with the evolution of moiré period. The Raman intensity ratio as a function of twisting angle follows an exponential profile matching the moiré period with two local maxima at 0° and 60° and a minimum at 30°. Using a series of temperature-dependent Raman and photoluminescence (PL) measurements as well as \textit{ab initio} calculations, the intensity ratio $I_{B_{2g}}/I_{E_{2g}/{A_{1g}}}$ is explained as a signature of lattice dynamics in tB WSe$_2$ moiré superlattices. By further exploring different material combinations of twisted hetero-bilayers, the results are extended for all kinds of Mo- and W-based TMDCs.
Artificially constructed van der Waals heterostructures (vdWHs) provide an ideal platform for realizing emerging quantum phenomena in condensed matter physics. Two methods for building vdWHs have been developed: stacking two-dimensional (2D) materials into a bilayer structure with different lattice constants, or with different orientations. The interlayer coupling stemming from commensurate or incommensurate superlattice pattern plays an important role in vdWHs for modulating the band structures and generating new electronic states. In this article, we review a series of novel quantum states d…
Elastic properties of materials are an important factor in their integration in applications. Chemical vapor deposited (CVD) monolayer semiconductors are proposed as key components in industrial-scale flexible devices and building blocks of 2D van der Waals heterostructures. However, their mechanical and elastic properties have not been fully characterized. Here we report high 2D elastic moduli of CVD monolayer MoS2 and WS2 (~ 170 N/m), which is very close to the value of exfoliated MoS2 monolayers and almost half the value of the strongest material, graphene. The 2D moduli of their bilayer he…
In this paper, we employ a fully microscopic approach to the study of interlayer excitons in hetero-bilayers. We use Fowler's and Karplus' method to access the dynamical polarizability of non--interacting interlayer excitons in a $\mathrm{WSe}_{2}/\mathrm{WS}_{2}$--based van der Waals heterostructure. Following from the calculation of the linear polarizability, we consider Svendsen's variational method to the calculation of the dynamic third--order polarizability. With this variational method, we study both two--photon absorption and third--harmonic generation processes for interlayer excitons…
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…
Using full-potential density functional calculations within local density approximation (LDA), we predict that mechanically tunable band-gap and quasi-particle-effective-mass are realizable in graphene/hexagonal-BN hetero-bilayer (C/h-BN HBL) by application of in-plane homogeneous biaxial strain. While providing one of the possible reasons for the experimentally observed gap-less pristine-graphene-like electronic properties of C/h-BN HBL, which theoretically has a narrow band-gap, we suggest a schematic experiment for verification of our results which may find applications in nano-electromecha…
Among the van der Waals heterostructures, graphene/h-BN heterostructure is an appropriate candidate for 2D nanoelectronic devices. In this paper, using non-equilibrium molecular dynamics simulation approach, heat transport in bilayer graphene/h-BN and graphene/h-BN van der Waals heterostructure (i.e. h-BN flakes periodically inserted on the top and bottom of a graphene layer) are explored. The results show that by increasing the length of the system, the thermal conductivity of bilayer graphene/h-BN increases. Furthermore, it was revealed that heat transport in graphene/h-BN heterostructure en…
Twisted bilayers of two-dimensional materials, such as twisted bilayer graphene, often feature flat electronic bands that enable the observation of electron correlation effects. In this work, we study the electronic structure of twisted transition metal dichalcogenide (TMD) homo- and heterobilayers that are obtained by combining MoS$_2$, WS$_2$, MoSe$_2$ and WSe$_2$ monolayers, and show how flat band properties depend on the chemical composition of the bilayer as well as its twist angle. We determine the relaxed atomic structure of the twisted bilayers using classical force fields and calculat…
Very recently, twisted graphene bilayer (TGB) around the first magic angle 1.1° has attracted much attention for the realization of exotic quantum states, such as correlated insulator behavior and unconventional superconductivity. Here we elaborately studied a series of TGBs around the first magic angle engineered by heterostrain, where each layer is strained independently. Our experiment indicated that a moderate heterostrain enables the structural evolution from the small-angle TGB ( ~ 1.5°) to the strained magic-angle TGB (θ ~ 1.1°), exhibiting the characteristic low-energy flat bands. The …
We demonstrate gate-tunable resonant tunneling and negative differential resistance between two rotationally aligned bilayer graphene sheets separated by bilayer WSe2. We observe large interlayer current densities of 2 uA/um2 and 2.5 uA/um2, and peak-to-valley ratios approaching 4 and 6 at room temperature and 1.5 K, respectively, values that are comparable to epitaxially grown resonant tunneling heterostructures. An excellent agreement between theoretical calculations using a Lorentzian spectral function for the two-dimensional (2D) quasiparticle states, and the experimental data indicates th…
We demonstrate a new technique for creating unique forms of pure sp2-bonded carbon and unprecedented hetero-molecules. These new structures, which we refer to as sculpturenes, are formed by sculpting selected shapes from bilayer graphene, hetero-bilayers or multi-layered materials and allowing the shapes to spontaneously reconstruct. The simplest sculpturene is topologically equivalent to a torus, with dimensions comparable to those of fullerenes. The topology of these new molecular structures is stable against atomic scale defects.
We study the effects of heterostrain on moiré bands in twisted bilayer graphene and bilayer transition metal dichalcogenide (TMD) systems. For bilayer graphene with twist angle near $1^\circ$, we show that heterostrain significantly increases the energy separation between conduction and valence bands as well as the Dirac velocity at charge neutrality, which resolves several puzzles in scanning tunneling spectroscopy and quantum oscillation experiments at once. For bilayer TMD, we show that applying small heterostrain generally leads to flat moiré bands that are highly tunable.
Twisted van der Waals heterostructures unravel a new platform to study strongly correlated quantum phases. The interlayer coupling in these heterostructures is sensitive to twist angles ($θ$) and key to controllably tune several exotic properties. Here, we demonstrate a systematic evolution of the interlayer coupling strength with twist angle in bilayer $\mathrm{MoS_{2}}$ using a combination of Raman spectroscopy and classical simulations. At zero doping, we show a \textit{monotonic} increment of the separation between the $\mathrm{A_{1g}}$ and $\mathrm{E^{1}_{2g}}$ mode frequencies as $θ$ dec…
Twist engineering, or the alignment of two-dimensional (2D) crystalline layers with desired orientations, has led to tremendous success in modulating the charge degree of freedom in hetero- and homo-structures, in particular, in achieving novel correlated and topological electronic phases in moiré electronic crystals. However, although pioneering theoretical efforts have predicted nontrivial magnetism and magnons out of twisting 2D magnets, experimental realization of twist engineering spin degree of freedom remains elusive. Here, we leverage the archetypal 2D Ising magnet chromium triiodide (…
The twist angle in transition metal dichalcogenide (TMD) heterobilayers is a compelling degree of freedom that determines electron correlations and the period of lateral confinement of moiré excitons. Here we perform polarization-resolved second harmonic generation (SHG) spectroscopy of MoS2/WSe2 heterostructures. We demonstrate that by choosing suitable laser energies the twist angle between two monolayers can be measured directly on the assembled heterostructure. We show that the amplitude and polarization of the SHG signal from the heterostructure are determined by the twist angle between t…
Magnetic properties of thin films differs from that of the corresponding bulk materials and show novel physics as a result of their reduced size and dimensionality. Profound changes in magnetic properties can also result with exchange bias between the interface of the thin films of different materials. Here we present Fe$_3$O$_4$, Gd$_5$Si$_4$ and Fe$_3$O$_4$-Gd$_5$Si$_4$ bilayer thin films of varying thicknesses were prepared by RF Magnetron sputtering of Fe$_3$O$_4$ and Gd$_5$Si$_4$ targets on silicon substrates in high vacuum. Their magnetization was measured at room temperature in fields o…
We study the electronic structure of a heterojunction made of two monolayers of MoS2 and WS2. Our first-principles density functional calculations show that, unlike in the homogeneous bilayers, the heterojunction has an optically active band-gap, smaller than the ones of MoS2 and WS2 single layers. We find that that the optically active states of the maximum valence and minimum conduction bands are localized on opposite monolayers, and thus the lowest energy electron-holes pairs are spatially separated. Our findings portrait the MoS2-WS2 bilayer as a prototypical example for band-gap engineeri…
A Wigner crystal, a regular electron lattice arising from strong correlation effects, is one of the earliest predicted collective electronic states. This many-body state exhibits quantum and classical phase transitions and has been proposed as a basis for quantum information processing applications. In semiconductor platforms, two-dimensional Wigner crystals have been observed under magnetic field or moiré-based lattice potential where the electron kinetic energy is strongly suppressed. Here, we report bilayer Wigner crystal formation without a magnetic or confinement field in atomically thin …
A major theoretical challenge of studying twisted transition metal dichalcogenide (TMD) bilayers is that the unit cell of such structures is very large and therefore difficult to address using first-principles methods. However, twisted TMD bilayers form moiré patterns, which consist of regions of commensurate stacking, either smoothly interpolated into one another or separated by sharp domain walls. In this paper, we study twisted TMD bilayers by studying the properties of the constituent commensurate structures. Using density functional theory (DFT), we compute band structures for commensurat…
Two-dimensional helical superconductivity and gapless superconducting edge modes in the 1T$^\prime$-WS$_2$/2H-WS$_2$ heterophase bilayer
University of California, Santa Barbara（加州大学圣塔芭芭拉分校）；Brookhaven National Laboratory（布鲁海文国家实验室）；Stony Brook University（石溪大学）；Flatiron Institute（平顿研究所）；University of Wisconsin-Madison（威斯康星大学麦迪逊分校）；University of Nevada, Reno（内华达大学里诺分校）
Van der Waals heteroepitaxy allows deterministic control over lattice mismatch or azimuthal orientation between atomic layers to produce long wavelength superlattices. The resulting electronic phases depend critically on the superlattice periodicity as well as localized structural deformations that introduce disorder and strain. Here, we introduce Bragg interferometry, based on four-dimensional scanning transmission electron microscopy, to capture atomic displacement fields in twisted bilayer graphene with twist angles < 2°. Nanoscale spatial fluctuations in twist angle and uniaxial heterostra…
Twisted multilayers of two-dimensional (2D) materials are an increasingly important platform for investigating quantum phases of matter, and in particular, strongly correlated electrons. The moiré pattern introduced by the relative twist between layers creates effective potentials of long-wavelength, leading to electron localization. However, in contrast to the abundance of 2D materials, few twisted heterostructures have been studied until now. Here we develop a first-principle continuum theory to study the electronic bands introduced by moire patterns of twisted Janus transition metal dichalc…
We introduce an approach to derive realistic Coulomb interaction terms in free standing layered materials and vertical heterostructures from ab-initio modelling of the corresponding bulk materials. To this end, we establish a combination of calculations within the framework of the constrained random phase approximation, Wannier function representation of Coulomb matrix elements within some low energy Hilbert space and continuum medium electrostatics, which we call Wannier function continuum electrostatics (WFCE). For monolayer and bilayer graphene we reproduce full ab-initio calculations of th…
A variety of correlated phases have recently emerged in select twisted van der Waals (vdW) heterostructures owing to their flat electronic dispersions. In particular, heterostructures of twisted double bilayer graphene (tDBG) manifest electric field-tunable correlated insulating (CI) states at all quarter fillings of the conduction band, accompanied by nearby states featuring signatures suggestive of superconductivity. Here, we report electrical transport measurements of tDBG in which we elucidate the fundamental role of spontaneous symmetry breaking within its correlated phase diagram. We obs…
Van der Waals heterostructures obtained by artificially stacking two-dimensional crystals represent the frontier of material engineering, demonstrating properties superior to those of the starting materials. Fine control of the interlayer twist angle has opened new possibilities for tailoring the optoelectronic properties of these heterostructures. Twisted bilayer graphene with a strong interlayer coupling is a prototype of twisted heterostructure inheriting the intriguing electronic properties of graphene. Understanding the effects of the twist angle on its out-of-equilibrium optical properti…
In this paper, we derive lattice models for the narrow moiré bands of the AB-stacked twisted WSe$_2$ homobilayer through continuum model and Wannier orbital construction. Previous work has shown that an approximate SU(4) Hubbard model may be realized by combining spin and layer because inter-layer tunneling is suppressed due to spin $S_z$ conservation. However, Rashba spin-orbit coupling (SOC) was ignored in the previous analysis. Here, we show that a Rashba SOC of reasonable magnitude can induce a finite but very small inter-layer hopping in the final lattice Hubbard model. At total filling $…
