Interlayer Twist Research Articles

Graphene-based spinmechatronic valve

The interlayer twist between van der Waals graphene crystals led to the discovery of superconducting and insulating states near the magic angle. In this work, we exploit this mechanical degree of freedom by twisting the graphene middle layer in a trilayer graphene spacer between two metallic leads (magnetic and nonmagnetic). A large difference in conductance is found depending on the angle of twist between the middle layer graphene and the ones at the interface. This difference, called twisting resistance, reach more than 1000% in the non-magnetic Cu case. For the magnetic Ni case, the magneto-resistance decreases and the difference in conductance between twisted and not twisted depends strongly on the relative magnetization configuration. For the parallel configuration, the twisting resistance is about −40%, while for the anti-parallel configuration it can reach up to 130%. Furthermore, we show that the twisting resistance can be enhanced by inserting a thin Cu layer at the interface of Ni/graphene where it reaches a value of 200% and 1600% for parallel and antiparallel configurations, respectively. These findings could pave the way toward the integration of 2D materials on novel spinmechatronics based devices.

Direct growth of mm-size twisted bilayer graphene by plasma-enhanced chemical vapor deposition

Plasma enhanced chemical vapor deposition (PECVD) techniques have been shown to be an efficient method to achieve single-step synthesis of high-quality monolayer graphene (MLG) without the need of active heating. Here we report PECVD-growth of single-crystalline hexagonal bilayer graphene (BLG) flakes and mm-size BLG films with the interlayer twist angle controlled by the growth parameters. The twist angle has been determined by three experimental approaches, including direct measurement of the relative orientation of crystalline edges between two stacked monolayers by scanning electron microscopy, analysis of the twist angle-dependent Raman spectral characteristics, and measurement of the Moiré period with scanning tunneling microscopy. In mm-sized twisted BLG (tBLG) films, the average twist angle can be controlled from 0° to approximately 20°, and the angular spread for a given growth condition can be limited to < 7°. Different work functions between MLG and BLG have been verified by the Kelvin probe force microscopy and ultraviolet photoelectron spectroscopy. Electrical measurements of back-gated field-effect-transistor devices based on small-angle tBLG samples revealed high-quality electric characteristics at 300 K and insulating temperature dependence down to 100 K. This controlled PECVD-growth of tBLG thus provides an efficient approach to investigate the effect of varying Moiré potentials on tBLG.

Quantum Hall Effect Measurement of Spin-Orbit Coupling Strengths in Ultraclean Bilayer Graphene/WSe2 Heterostructures.

We study proximity-induced spin-orbit coupling (SOC) in bilayer graphene/few-layer WSe2 heterostructure devices. Contact mode atomic force microscopy (AFM) cleaning yields ultraclean interfaces and high-mobility devices. In a perpendicular magnetic field, we measure the quantum Hall effect to determine the Landau level structure in the presence of out-of-plane Ising and in-plane Rashba SOC. A distinct Landau level crossing pattern emerges when tuning the charge density and displacement field independently with dual gates, originating from a layer-selective SOC proximity effect. Analyzing the Landau level crossings and measured inter-Landau level energy gaps yields the proximity-induced SOC energy scale. The Ising SOC is ∼2.2 meV, 100 times higher than the intrinsic SOC in graphene, whereas its sign is consistent with theories predicting a dependence of SOC on interlayer twist angle. The Rashba SOC is ∼15 meV. Finally, we infer the magnetic field dependence of the inter-Landau level Coulomb interactions. These ultraclean bilayer graphene/WSe2 heterostructures provide a high mobility system with the potential to realize novel topological electronic states and manipulate spins in nanostructures.

Charge order and broken rotational symmetry in magic-angle twisted bilayer graphene

Bilayer graphene can be modified by rotating (twisting) one layer with respect to the other. The interlayer twist gives rise to a moiré superlattice that affects the electronic motion and alters the band structure1-4. Near a 'magic angle' of twist2,4, where the emergence of a flat band causes the charge carriers to slow down3, correlated electronic phases including Mott-like insulators and superconductors were recently discovered5-8 by using electronic transport. These measurements revealed an intriguing similarity between magic-angle twisted bilayer graphene and high-temperature superconductors, which spurred intensive research into the underlying physical mechanism9-14. Essential clues to this puzzle, such as the symmetry and spatial distribution of the spectral function, can be accessed through scanning tunnelling spectroscopy. Here we use scanning tunnelling microscopy and spectroscopy to visualize the local density of states and charge distribution in magic-angle twisted bilayer graphene. Doping the sample to partially fill the flat band, we observe a pseudogap phase accompanied by a global stripe charge order that breaks the rotational symmetry of the moiré superlattice. Both the pseudogap and the stripe charge order disappear when the band is either empty or full. The close resemblance to similar observations in high-temperature superconductors15-21 provides new evidence of a deeper link underlying the phenomenology of these systems.

Maximized electron interactions at the magic angle in twisted bilayer graphene

The electronic properties of heterostructures of atomically thin van der Waals crystals can be modified substantially by moiré superlattice potentials from an interlayer twist between crystals1,2. Moirétuning of the band structure has led to the recent discovery of superconductivity3,4 and correlated insulating phases5 in twisted bilayer graphene (TBG) near the 'magic angle' of twist of about 1.1 degrees, with a phase diagram reminiscent of high-transition-temperature superconductors. Here we directly map the atomic-scale structural and electronic properties of TBG near the magic angle using scanning tunnelling microscopy and spectroscopy. We observe two distinct van Hove singularities (VHSs) in the local density of states around the magic angle, with an energy separation of 57millielectronvolts that drops to 40millielectronvolts with high electron/hole doping. Unexpectedly, the VHS energy separation continues to decrease with decreasing twist angle, with a lowest value of 7 to 13 millielectronvolts at a magic angle of 0.79 degrees. More crucial to the correlated behaviour of this material, we find that at the magic angle, the ratio of the Coulomb interaction to the bandwidth of each individual VHS (U/t) is maximized, which is optimal for electronic Cooper pairing mechanisms. When doped near the half-moiré-band filling, a correlation-induced gap splits the conduction VHS with a maximum size of 6.5 millielectronvolts at 1.15 degrees, dropping to 4 millielectronvolts at 0.79 degrees. We capture the doping-dependent and angle-dependent spectroscopy results using a Hartree-Fock model, which allows us to extract the on-site and nearest-neighbour Coulomb interactions. This analysis yields a U/t of order unity indicating that magic-angle TBG is moderately correlated. In addition, scanning tunnelling spectroscopy maps reveal an energy- and doping-dependent three-fold rotational-symmetry breaking of the local density of states in TBG, with the strongest symmetry breaking near the Fermi level and further enhanced when doped to the correlated gap regime. This indicates the presence of a strong electronic nematic susceptibility or even nematic order in TBG in regions of the phase diagram where superconductivity is observed.

Stacking, strain, and twist in 2D materials quantified by 3D electron diffraction

The field of two-dimensional (2D) materials has expanded to multilayered systems where electronic, optical, and mechanical properties change-often dramatically-with stacking order, thickness, twist, and interlayer spacing [1-5]. For transition metal dichalcogenides (TMDs), bond coordination within a single van der Waals layer changes the out-of-plane symmetry that can cause metal-insulator transitions [1, 6] or emergent quantum behavior [7]. Discerning these structural order parameters is often difficult using real-space measurements, however, we show 2D materials have distinct, conspicuous three-dimensional (3D) structure in reciprocal space described by near infinite oscillating Bragg rods. Combining electron diffraction and specimen tilt we probe Bragg rods in all three dimensions to identify multilayer structure with sub-Angstrom precision across several 2D materials-including TMDs (MoS2, TaSe2, TaS2) and multilayer graphene. We demonstrate quantitative determination of key structural parameters such as surface roughness, inter- & intra-layer spacings, stacking order, and interlayer twist using a rudimentary transmission electron microscope (TEM). We accurately characterize the full interlayer stacking order of multilayer graphene (1-, 2-, 6-, 12-layers) as well the intralayer structure of MoS2 and extract a chalcogen-chalcogen layer spacing of 3.07 +/- 0.11 Angstrom. Furthermore, we demonstrate quick identification of multilayer rhombohedral graphene.

Tunable photoluminescence of bilayer MoS2 via interlayer twist

Atomically thin molybdenum disulfide (MoS2) has been treated as a promising optoelectronic material, due to its strong photoluminescence (PL) emission. Here, we demonstrate the tunability of the PL properties of bilayer MoS2 through interlayer twist. The PL emission peak position, full-width-at-half-maximum (FWHM) and intensity are found to be dependent on the twisted angle, which reach their extremum for the twisted angle around 40°. This PL modulation is attributed to the change of the interlayer coupling between the adjacent MoS2 layers. In addition, peak A splitting of PL spectra is found in twisted bilayer MoS2, due to the doping effect from substrate. These results enrich our understanding of the relationship between PL emission and interlayer coupling, which is significant for optical and electrical applications of twisted bilayer MoS2 (tBLM).

Chiral twisted van der Waals nanowires.

Van der Waals heterostructures with small misalignment between adjacent layers ('interlayer twist') are of interest because of electronic structure and correlation phenomena (such as superconductivity) that are determined by both the atomic lattice and long-range superlattice potentials arising in interlayer moiré patterns1-7. Previously, such twisted heterostructures have involved a single planar interface between layers isolated by exfoliation and micromechanically stacked in the desired relative orientation1,8-12. Here we demonstrate a class of materials-van der Waals nanowires of layered crystals-in which a tunable interlayer twist evolves naturally during synthesis. In vapour-liquid-solid growth, nanowires of germanium(II) sulfide, an anisotropic layered semiconductor, crystallize with layering along the wire axis13 and have a strong propensity for forming axial screw dislocations. Nanometre-resolved electron diffraction shows that Eshelby twist, induced by a torque on the ends of a cylindrical solid due to the stress field of an axial dislocation14,15, causes a chiral structure in the van der Waals nanowires. The in-plane germanium sulfide crystal axes progressively rotate along the wire, and germanium sulfide layers in adjacent turns of the helix naturally form a moiré pattern because of their interlayer twist. The axial rotation and the twist are tunable by varying the nanowire thickness. Combined electron diffraction and cathodoluminescence spectroscopy show the correlation between the interlayer twist and locally excited light emission that is due to progressive changes in the lattice orientation and in the interlayer moiré registry along the nanowires. The findings demonstrate a step towards scalable fabrication of van der Waals structures with defined twist angles, in which interlayer moiré patterns are realized along a helical path on a nanowire instead of a planar interface.

Atomic and electronic reconstruction at the van der Waals interface in twisted bilayer graphene.

Control of the interlayer twist angle in two-dimensional van der Waals (vdW) heterostructures enables one to engineer a quasiperiodic moiré superlattice of tunable length scale1-8. In twisted bilayer graphene, the simple moiré superlattice band description suggests that the electronic bandwidth can be tuned to be comparable to the vdW interlayer interaction at a 'magic angle'9, exhibiting strongly correlated behaviour. However, the vdW interlayer interaction can also cause significant structural reconstruction at the interface by favouring interlayer commensurability, which competes with the intralayer lattice distortion10-16. Here we report atomic-scale reconstruction in twisted bilayer graphene and its effect on the electronic structure. We find a gradual transition from an incommensurate moiré structure to an array of commensurate domains with soliton boundaries as we decrease the twist angle across the characteristic crossover angle, θc ≈ 1°. In the solitonic regime (θ < θc) where the atomic and electronic reconstruction become significant, a simple moiré band description breaks down and the secondary Dirac bands appear. On applying a transverse electric field, we observe electronic transport along the network of one-dimensional topological channels that surround the alternating triangular gapped domains. Atomic and electronic reconstruction at the vdW interface provide a new pathway to engineer the system with continuous tunability.

How interlayer twist angles affect in-plane and cross-plane thermal conduction of multilayer graphene: A non-equilibrium molecular dynamics study

Graphene, a kind of emerging low dimensional carbon material, has admirable thermal properties with potential applications in the thermal management of aerospace and microelectronics fields. In recent studies, thermal properties of both conventional single-layer and multilayer graphene were extensively studied. However, few studies focused on that of multilayer graphene with twist angles, whose thermal properties are different from that of conventional graphene because of the existence of interlayer twist angles. Such knowledge gap hinders the potential applications. Therefore, the thermal conductivity of bilayer, 4-layers and 6-layer zigzag graphene with various twist angles is investigated utilizing non-equilibrium molecular dynamics at the typical temperature region in this study, and both in- and cross-plane thermal conductivity are investigated. The size of the studied graphene is 10 nm × 22 nm in the x-y plane, and the size in the z-direction depends on the number of layers. Moreover, the phonon vibrational density of state is also analyzed for mechanisms behind the thermal transport. The result indicates that a local maximum value can be found with the twist angle of 30° for in-plane thermal conduction. The results also suggest that the highest thermal conductivity could be reached without any twist angles for both in and cross-plane conduction. The observation would provide an opportunity to study the characteristics of in-plane and cross-plane thermal transport of twisted multilayer graphene.

Interlayer hybridization and moiré superlattice minibands for electrons and excitons in heterobilayers of transition-metal dichalcogenides

Geometrical moir\'e patterns, generic for almost aligned bilayers of two-dimensional (2D) crystals with similar lattice structure but slightly different lattice constants, lead to zone folding and miniband formation for electronic states. Here, we show that moir\'e superlattice (mSL) effects in $\mathrm{MoSe}_2/\mathrm{WS}_2$ and $\mathrm{MoTe}_2/\mathrm{MoSe}_2$ heterobilayers that feature alignment of the band edges are enhanced by resonant interlayer hybridization, and anticipate similar features in twisted homobilayers of TMDs, including examples of narrow minibands close to the actual band edges. Such hybridization determines the optical activity of interlayer excitons in transition-metal dichalcogenide (TMD) heterostructures, as well as energy shifts in the exciton spectrum. We show that the resonantly hybridized exciton (hX) energy should display a sharp modulation as a function of the interlayer twist angle, accompanied by additional spectral features caused by umklapp electron-photon interactions with the mSL. We analyze the appearance of resonantly enhanced mSL features in absorption and emission of light by the interlayer exciton hybridization with both intralayer A and B excitons in $\mathrm{MoSe}_2/\mathrm{WS}_2$, $\mathrm{MoTe}_2/\mathrm{MoSe}_2$, $\mathrm{MoSe}_2/\mathrm{MoS}_2$, $\mathrm{WS}_2/\mathrm{MoS}_2$, and $\mathrm{WSe}_2/\mathrm{MoSe}_2$.

Linking interlayer twist angle to geometrical parameters of self-assembled folded graphene structures

Thin adhesive films can be removed from substrates, torn, and folded in distinct geometries under external driving forces. In two-dimensional materials, however, these processes can be self-driven as shown in previous studies on folded twisted bilayer graphene nanoribbons produced by spontaneous tearing and peeling from a substrate. Here, we use atomic force microscopy techniques to generate and characterize the geometrical structure of naturally self-grown folded nanoribbon structures. Measurements of nanoribbon width and interlayer separation reveal similar twist-angle dependences possibly caused by the anisotropy in the bilayer potential. In addition, analysis of the data shows an unexpected correlation between the height of the folded arc edge—parameterized by a radius R—, and the ribbon width, suggestive of a self-growth process driven by a variable cross-sectional shape. These observations are well described by an energy minimization model that includes the bilayer adhesion energy density as represented by a distance dependent Morse potential. We obtain an analytical expression for the radius R versus the ribbon width that predicts a renormalized bending rigidity and stands in good agreement with experimental observations. The newly found relation between these geometrical parameters suggests a mechanism for tailored growth of folded twisted bilayer graphene- a platform for many intriguing physics phenomena.

Negative circular polarization emissions from WSe2/MoSe2 commensurate heterobilayers

Van der Waals heterobilayers of transition metal dichalcogenides with spin–valley coupling of carriers in different layers have emerged as a new platform for exploring spin/valleytronic applications. The interlayer coupling was predicted to exhibit subtle changes with the interlayer atomic registry. Manually stacked heterobilayers, however, are incommensurate with the inevitable interlayer twist and/or lattice mismatch, where the properties associated with atomic registry are difficult to access by optical means. Here, we unveil the distinct polarization properties of valley-specific interlayer excitons using epitaxially grown, commensurate WSe2/MoSe2 heterobilayers with well-defined (AA and AB) atomic registry. We observe circularly polarized photoluminescence from interlayer excitons, but with a helicity opposite to the optical excitation. The negative circular polarization arises from the quantum interference imposed by interlayer atomic registry, giving rise to distinct polarization selection rules for interlayer excitons. Using selective excitation schemes, we demonstrate the optical addressability for interlayer excitons with different valley configurations and polarization helicities.

Nanoscale Probing of Interaction in Atomically Thin Layered Materials.

We combine conductive atomic force microscopy (CAFM) and molecular dynamics (MD) simulations to reveal the interaction of atomically thin layered materials (ATLMs) down to nanoscale lateral dimension. The setup also allows quantifying, for the first time, the effect of layer number and electric field on the dielectric constant of ATLMs with few-layer down to monolayer thickness. Our CAFM-assisted electrostatic technique shows that high-quality mono- and bilayer graphene is reliably produced at significant yields only by the shear type of bond breaking between layers, whereas the normal type of bond breaking exhibits a very stochastic process mainly due to the coexistence of local delamination and interlayer twist. Our dielectric constant measurements also reveal a very weak dependence on the layer number and the electric field (up to our experimental limit of 0.1 V/Å), which is in contrast with theoretical reports. Owing to unexpectedly large variations in the screening ability of pristine monolayer graphene under ambient conditions, we further demonstrate that the effective dielectric constant of monolayer graphene can be engineered to provide a broad spectrum of dielectric responses (3.5–17) through oxidation and thermal annealing, thus confirming its much higher chemical reactivity than bilayer and few layers.

Robust Stacking-Independent Ultrafast Charge Transfer in MoS2/WS2 Bilayers.

Van der Waals-coupled two-dimensional (2D) heterostructures have attracted great attention recently due to their high potential in the next-generation photodetectors and solar cells. The understanding of charge-transfer process between adjacent atomic layers is the key to design optimal devices as it directly determines the fundamental response speed and photon-electron conversion efficiency. However, general belief and theoretical studies have shown that the charge transfer behavior depends sensitively on interlayer configurations, which is difficult to control accurately, bringing great uncertainties in device designing. Here we investigate the ultrafast dynamics of interlayer charge transfer in a prototype heterostructure, the MoS2/WS2 bilayer with various stacking configurations, by optical two-color ultrafast pump-probe spectroscopy. Surprisingly, we found that the charge transfer is robust against varying interlayer twist angles and interlayer coupling strength, in time scale of ∼90 fs. Our observation, together with atomic-resolved transmission electron characterization and time-dependent density functional theory simulations, reveals that the robust ultrafast charge transfer is attributed to the heterogeneous interlayer stretching/sliding, which provides additional channels for efficient charge transfer previously unknown. Our results elucidate the origin of transfer rate robustness against interlayer stacking configurations in optical devices based on 2D heterostructures, facilitating their applications in ultrafast and high-efficient optoelectronic and photovoltaic devices in the near future.

Plasmon-assisted resonant tunneling in graphene-based heterostructures

We develop a theory of electron tunneling accompanied by carrier-carrier scattering in graphene - insulator - graphene heterostructures. Due to the dynamic screening of Coulomb interaction, the scattering-aided tunneling is resonantly enhanced if the transferred energy and momentum correspond to those of surface plasmons. We reveal the possible experimental manifestations of such plasmon-assisted tunneling in current-voltage curves and plasmon emission spectra of graphene-based tunnel junctions. We find that inelastic current and plasmon emission rates have sharp peaks at voltages providing equal energies, momenta and group velocities of plasmons and interlayer single-particle excitations. The strength of this resonance, which we call plasmaronic resonance, is limited by interlayer twist and plasmon lifetime. The onset of plasmon-assisted tunneling can be also marked by a cusp in the junction $I(V)$-curve at low temperatures, and the threshold voltage for such tunneling weakly depends on carrier density and persists in the presence of interlayer twist.

Gate induced monolayer behavior in twisted bilayer black phosphorus

Optical and electronic properties of black phosphorus strongly depend on the number of layers and type of stacking. Using first-principles calculations within the framework of density functional theory, we investigate the electronic properties of bilayer black phosphorus with an interlayer twist angle of 90°. These calculations are complemented with a simple model which is able to capture most of the low energy features and is valid for arbitrary twist angles. The electronic spectrum of 90° twisted bilayer black phosphorus is found to be x-y isotropic in contrast to the monolayer. However x-y anisotropy, and a partial return to monolayer-like behavior, particularly in the valence band, can be induced by an external out-of-plane electric field. Moreover, the preferred hole effective mass can be rotated by 90° simply by changing the direction of the applied electric field. In particular, a 0.4 (−0.4) V out-of-plane electric field results in a ∼60% increase in the hole effective mass along the () axis and enhances the () ratio as much as by a factor of 40. Our DFT and simulations clearly indicate that the twist angle in combination with an appropriate gate voltage is a novel way to tune the electronic and optical properties of bilayer phosphorus and it gives us a new degree of freedom to engineer the properties of black phosphorus based devices.

Coincidence Lattices and Interlayer Twist in van der Waals Heterostructures: Application of the Coincidence Lattice Method on $$\hbox {hBN/MoSe}_2$$ hBN/MoSe 2 Heterobilayer Systems

Van der Waals heterostructures have great potential in large-scale integration devices and exploration of new physics. Experimental investigations allow flexible combinations of two-dimensional crystals in device fabrications. Theory, however, has limitations of supercell sizes and commensurability, translated into computational effort. In this work, we demonstrate the application of the coincidence lattice method to simulate two \(\hbox {hBN/MoSe}_2\) heterobilayers taking interlayer twist effects into account. We predict that both systems are stable upon contact and interact via van der Waals dispersions. We found that electronic properties of \(\hbox {MoSe}_2\) are preserved for both simulated systems, but hBN suffers from the increase of interface interactions, as evidenced by band structures and density of states calculations. Finally, band discontinuities are obtained and charge transfer arguments explain small shifts in band offsets with respect to natural alignments. We conclude that hBN is a reasonable substrate for preserving useful properties of \(\hbox {MoSe}_2\) for application in electronic and optoelectronic devices, and that interlayer twist angles play a significant role in the physics of van der Waals heterostructures.

Gate Switchable Transport and Optical Anisotropy in 90° Twisted Bilayer Black Phosphorus

Anisotropy describes the directional dependence of a material's properties such as transport and optical response. In conventional bulk materials, anisotropy is intrinsically related to the crystal structure and thus not tunable by the gating techniques used in modern electronics. Here we show that, in bilayer black phosphorus with an interlayer twist angle of 90°, the anisotropy of its electronic structure and optical transitions is tunable by gating. Using first-principles calculations, we predict that a laboratory-accessible gate voltage can induce a hole effective mass that is 30 times larger along one Cartesian axis than along the other axis, and the two axes can be exchanged by flipping the sign of the gate voltage. This gate-controllable band structure also leads to a switchable optical linear dichroism, where the polarization of the lowest-energy optical transitions (absorption or luminescence) is tunable by gating. Thus, anisotropy is a tunable degree of freedom in twisted bilayer black phosphorus.

Resonant tunneling and the quasiparticle lifetime in graphene/boron nitride/graphene heterostructures

Tunneling of quasiparticles between two nearly aligned graphene sheets produces resonant current-voltage characteristics because of the quasiexact conservation of in-plane momentum. We claim that, in this regime, vertical transport in graphene/boron nitride/graphene heterostructures carries precious information on electron-electron interactions and the quasiparticle spectral function of the two-dimensional electron system in graphene. We present extensive microscopic calculations of the tunneling spectra with the inclusion of quasiparticle lifetime effects and elucidate the range of parameters (interlayer bias, temperature, twist angle, and gate voltage) under which electron-electron interaction physics emerges.