Accurate Gap Determination in Monolayer and Bilayer Graphene/ h-BN Moiré Superlattices

Higher order gaps in the renormalized band structure of doubly aligned hBN/bilayer graphene moiré superlattice

This paper presents our findings on the recursive band gap engineering of chiral fermions in bilayer graphene doubly aligned with hBN. Using two interfering moiré potentials, we generate a supermoiré pattern that renormalizes the electronic bands of the pristine bilayer graphene, resulting in higher order fractal gaps even at very low energies. These Bragg gaps can be mapped using a unique linear combination of periodic areas within the system. To validate our findings, we use electronic transport measurements to identify the position of these gaps as a function of the carrier density. We establish their agreement with the predicted carrier densities and corresponding quantum numbers obtained using the continuum model. Our study provides strong evidence of the quantization of the momentum-space area of quasi-Brillouin zones in a minimally incommensurate lattice. It fills important gaps in the understanding of band structure engineering of Dirac fermions with a doubly periodic superlattice spinor potential.

Topological Flat Bands in Strained Graphene: Substrate Engineering and Optical Control

The discovery of correlated phases in twisted moiré superlattices accelerated the search for low-dimensional materials with exotic properties. A promising approach uses engineered substrates to strain the material. However, designing substrates for tailored properties is hindered by the incomplete understanding of the relationship between the substrate's shapes and the electronic properties of the deposited materials. By analyzing effective models of graphene under periodic deformations with generic crystalline profiles, we identify strong C2z symmetry breaking as the critical substrate geometric feature for emerging energy gaps and quasi-flat bands. We find continuous strain profiles producing connected pseudomagnetic field landscapes are important for band topology. We show that the resultant electronic and topological properties from a substrate can be controlled with circularly polarized light, which also offers unique signatures for identifying the band topology imprinted by strain. Our results can guide experiments on strain engineering for exploring interesting transport and topological phenomena.

Intrinsic Nonlinear Hall Effect and Gate-Switchable Berry Curvature Sliding in Twisted Bilayer Graphene

Though the observation of the quantum anomalous Hall effect and nonlocal transport response reveals nontrivial band topology governed by the Berry curvature in twisted bilayer graphene, some recent works reported nonlinear Hall signals in graphene superlattices that are caused by the extrinsic disorder scattering rather than the intrinsic Berry curvature dipole moment. In this Letter, we report a Berry curvature dipole induced intrinsic nonlinear Hall effect in high-quality twisted bilayer graphene devices. We also find that the application of the displacement field substantially changes the direction and amplitude of the nonlinear Hall voltages, as a result of a field-induced sliding of the Berry curvature hotspots. Our Letter not only proves that the Berry curvature dipole could play a dominant role in generating the intrinsic nonlinear Hall signal in graphene superlattices with low disorder densities, but also demonstrates twisted bilayer graphene to be a sensitive and fine-tunable platform for second harmonic generation and rectification.

Layer-Dependent Interaction Effects in the Electronic Structure of Twisted Bilayer Graphene Devices

Near the magic angle, strong correlations drive many intriguing phases in twisted bilayer graphene (tBG) including unconventional superconductivity and chern insulation. Whether correlations can tune symmetry breaking phases in tBG at intermediate (≳ 2°) twist angles remains an open fundamental question. Here, using ARPES, we study the effects of many-body interactions and displacement field on the band structure of tBG devices at an intermediate (3°) twist angle. We observe a layer- and doping-dependent renormalization of bands at the K points that is qualitatively consistent with moiré models of the Hartree-Fock interaction. We provide evidence of correlation-enhanced inversion symmetry-breaking, manifested by gaps at the Dirac points that are tunable with doping. These results suggest that electronic interactions play a significant role in the physics of tBG even at intermediate twist angles and present a new pathway toward engineering band structure and symmetry-breaking phases in moiré heterostructures.

General nonlinear Hall current in magnetic insulators beyond the quantum anomalous Hall effect

Can a generic magnetic insulator exhibit a Hall current? The quantum anomalous Hall effect (QAHE) is one example of an insulating bulk carrying a quantized Hall conductivity while insulators with zero Chern number present zero Hall conductance in the linear response regime. Here, we find that a general magnetic insulator possesses a nonlinear Hall conductivity quadratic to the electric field if the system breaks inversion symmetry, which can be identified as a new type of multiferroic coupling. This conductivity originates from an induced orbital magnetization due to virtual interband transitions. We identify three contributions to the wavepacket motion, a velocity shift, a positional shift, and a Berry curvature renormalization. In contrast to the crystalline solid, we find that this nonlinear Hall conductivity vanishes for Landau levels of a 2D electron gas, indicating a fundamental difference between the QAHE and the integer quantum Hall effect.

Signatures of hot carriers and hot phonons in the re-entrant metallic and semiconducting states of Moiré-gapped graphene

Stacking of graphene with hexagonal boron nitride (h-BN) can dramatically modify its bands from their usual linear form, opening a series of narrow minigaps that are separated by wider minibands. While the resulting spectrum offers strong potential for use in functional (opto)electronic devices, a proper understanding of the dynamics of hot carriers in these bands is a prerequisite for such applications. In this work, we therefore apply a strategy of rapid electrical pulsing to drive carriers in graphene/h-BN heterostructures deep into the dissipative limit of strong electron-phonon coupling. By using electrical gating to move the chemical potential through the "Moiré bands", we demonstrate a cyclical evolution between metallic and semiconducting states. This behavior is captured in a self-consistent model of non-equilibrium transport that considers the competition of electrically driven inter-band tunneling and hot-carrier scattering by strongly non-equilibrium phonons. Overall, our results demonstrate how a treatment of the dynamics of both hot carriers and hot phonons is essential to understanding the properties of functional graphene superlattices.

Heterostrain and temperature-tuned twist between graphene/h-BN bilayers

Two-dimensional materials stacked atomically at small twist angles enable the modification of electronic states, motivating twistronics. Here, we demonstrate that heterostrain can rotate the graphene flake on monolayer h-BN within a few degrees (- 4° to 4°), and the twist angle stabilizes at specific values with applied constant strains, while the temperature effect is negligible in 100-900 K. The band gaps of bilayers can be modulated from ~ 0 to 37 meV at proper heterostrain and twist angles. Further analysis shows that the heterostrain modulates the interlayer energy landscape by regulating Moiré pattern evolution. The energy variation is correlated with the dynamic instability of different stacking modes of bilayers, and arises from the fluctuation of interlayer repulsive interaction associated with p-orbit electrons. Our results provide a mechanical strategy to manipulate twist angles of graphene/h-BN bilayers, and may facilitate the design of rotatable electronic nanodevices.

Strong gate-tunability of flat bands in bilayer graphene due to moiré encapsulation between hBN monolayers

When using hexagonal boron-nitride (hBN) as a substrate for graphene, the resulting moiré pattern creates secondary Dirac points. By encapsulating a multilayer graphene within aligned hBN sheets the controlled moiré stacking may offer even richer benefits. Using advanced tight-binding simulations on atomistically-relaxed heterostructures, here we show that the gap at the secondary Dirac point can be opened in selected moiré-stacking configurations, and is independent of any additional vertical gating of the heterostructure. On the other hand, gating can broadly tune the gap at the principal Dirac point, and may thereby strongly compress the first moiré mini-band in width against the moiré-induced gap at the secondary Dirac point. We reveal that in hBN-encapsulated bilayer graphene this novel mechanism can lead to isolated bands flatter than 10 meV under moderate gating, hence presenting a convenient pathway towards electronically-controlled strongly-correlated states on demand.

Uncovering the Evolution of Low-Energy Plasmons in Nanopatterned Aluminum Plasmonics on Graphene

We report adjusting the charge-transfer-plasmon (CTP) resonances of aluminum (Al) bowties on suspended monolayer graphene via controlled nanofabrication and focused electron-beam irradiation. CTP resonances of bowties with a conductive junction blue-shift with an increase in junction width, whereas their 3λ/2 and λ resonances barely red-shift. These plasmon modes are derived and confirmed by an LC circuit model and electromagnetic simulations performed with boundary-element and frequency-domain methods. A monotonic decay of the CTP lifetime is observed, while the junction width is extended. Instead, the lifetimes of 3λ/2 and λ resonances are nearly independent of junction width. When the junction is shrunk by electron-beam irradiation, all antenna resonances red-shift. Having created an electron-beam-induced sub 5 nm gap in bowties, we monitor the unambiguous transition of a CTP into a bonding-type gap mode, which is highly sensitive to the separation distance. Meanwhile, the 3λ/2 and λ resonances evolve into dipolar bright and dipolar dark modes.

Robust Quantum Oscillation of Dirac Fermions in a Single-Defect Resonant Transistor

The massless nature of Dirac Fermions produces large energy gaps between Landau levels (LLs), which is promising for topological devices. While the energy gap between the zeroth and first LLs reaches 36 meV in a magnetic field of 1 T in graphene, exploiting the quantum Hall effect at room temperature requires large magnetic fields (∼30 T) to overcome the energy level broadening induced by charge inhomogeneities in the device. Here, we report a way to use the robust quantum oscillations of Dirac Fermions in a single-defect resonant transistor, which is based on local tunneling through a thin (∼1.4 nm) hexagonal boron nitride (h-BN) between lattice-orientation-aligned graphene layers. A single point defect in the h-BN, selected by the orientation-tuned graphene layers, probes local LLs in its proximity, minimizing the energy broadening of the LLs by charge inhomogeneity at a moderate magnetic field and ambient conditions. Thus, the resonant tunneling between lattice-orientation-aligned graphene layers highlights the potential to spectroscopically locate the atomic defects in the h-BN, which contributes to the study on electrically tunable single photon source via defect states in h-BN.

Theory of Correlated Insulators and Superconductivity in Twisted Bilayer Graphene

We introduce and analyze a model that sheds light on the interplay between correlated insulating states, superconductivity, and flavor-symmetry breaking in magic angle twisted bilayer graphene. Using a variational mean-field theory, we determine the normal-state phase diagram of our model as a function of the band filling. The model features robust insulators at even integer fillings, occasional weaker insulators at odd integer fillings, and a pattern of flavor-symmetry breaking at noninteger fillings. Adding a phonon-mediated intervalley retarded attractive interaction, we obtain strong-coupling superconducting domes, whose structure is in qualitative agreement with experiments. Our model elucidates how the intricate form of the interactions and the particle-hole asymmetry of the electronic structure determine the phase diagram. It also explains how subtle differences between devices may lead to the different behaviors observed experimentally. A similar model can be applied with minor modifications to other moiré systems, such as twisted trilayer graphene.

Lattice distortion-enhanced superlubricity of (Mo, X)S2 (X = Al, Ti, Cr and V) with moiré superlattice

Two-dimensional (2D) materials with the advantage of low interlayer shear strain are ultilized as lubricants in aerospace and precision manufacturing. Moiré superlattices (MSL), with attractive physical properties of electronic structures, interlayer hybridization and atomic forces, have been widely investigated in superlubricity, which is caused by elimination of interlayer lock-in by incommensurate atomic reconstruction. Although the foundations of superlubricity and the development of 2D lubricants via vanishing friction have been investigated, it is still important to comprehensively reveal the influence of MSL on the interlayer van der Waals (vdW) interactions of 2D lubricants. Here, the contributions of lattice distortions of solute-doped twisted bilayers (Mo, X)S₂ (X = Al, Ti, V and Cr) to superlubricity are comprehensively investigated by high-throughput modelling and DFT-D2 calculations. It is revealed that the lattice distortion not only breaks the interlayer balance of repulsion and van der Waals interactions but also yields layer corrugation. These layer-corrugation-induced changes of the interlayer interactions and spacing distances are utilized to optimize lubricity, which matches with the experimental friction coefficients in the order of (Mo, Al)S₂ > (Mo, Cr)S₂ > MoS₂ >(Mo, V)S₂ >(Mo, Ti)S₂. The evolutions of the band structures show an exponential relationship of the band edge width and layer deformations, paving a path to accelerate the development of advanced superlubricity materials via lattice distortions.

Direct probing of phonon mode specific electron-phonon scatterings in two-dimensional semiconductor transition metal dichalcogenides

Electron–phonon scatterings in solid-state systems are pivotal processes in determining many key physical quantities such as charge carrier mobilities and thermal conductivities. Here, we report direct probing of phonon mode specific electron–phonon scatterings in layered semiconducting transition metal dichalcogenides WSe₂, MoSe₂, WS₂, and MoS₂ through inelastic electron tunneling spectroscopy measurements, quantum transport simulations, and density functional calculation. We experimentally and theoretically characterize momentum-conserving single- and two-phonon electron–phonon scatterings involving up to as many as eight individual phonon modes in mono- and bilayer films, among which transverse, longitudinal acoustic and optical, and flexural optical phonons play significant roles in quantum charge flows. Moreover, the layer-number sensitive higher-order inelastic electron–phonon scatterings, which are confirmed to be generic in all four semiconducting layers, can be attributed to differing electronic structures, symmetry, and quantum interference effects during the scattering processes in the ultrathin semiconducting films.

Electron–phonon scattering events in solid-state systems determine key physical quantities. Here, the authors probe momentum-conserving single- and two-phonon electron–phonon scattering events involving up to as many as eight individual phonon modes in 2D semiconductors.

Strain-Induced Quantum Phase Transitions in Magic-Angle Graphene

We investigate the effect of uniaxial heterostrain on the interacting phase diagram of magic-angle twisted bilayer graphene. Using both self-consistent Hartree-Fock and density-matrix renormalization group calculations, we find that small strain values (ε∼0.1%-0.2%) drive a zero-temperature phase transition between the symmetry-broken "Kramers intervalley-coherent" insulator and a nematic semimetal. The critical strain lies within the range of experimentally observed strain values, and we therefore predict that strain is at least partly responsible for the sample-dependent experimental observations.

Accurate Measurement of the Gap of Graphene/h-BN Moiré Superlattice through Photocurrent Spectroscopy

Monolayer graphene aligned with hexagonal boron nitride (h-BN) develops a gap at the charge neutrality point (CNP). This gap has previously been extensively studied by electrical transport through thermal activation measurements. Here, we report the determination of the gap size at the CNP of graphene/h-BN superlattice through photocurrent spectroscopy study. We demonstrate two distinct measurement approaches to extract the gap size. A maximum of ∼14  meV gap is observed for devices with a twist angle of less than 1°. This value is significantly smaller than that obtained from thermal activation measurements, yet larger than the theoretically predicted single-particle gap. Our results suggest that lattice relaxation and moderate electron-electron interaction effects may enhance the CNP gap in graphene/h-BN superlattice.

Chirality-Induced Giant Unidirectional Magnetoresistance in Twisted Bilayer Graphene

Twisted bilayer graphene (TBG) exhibits fascinating correlation-driven phenomena like the superconductivity and Mott insulating state, with flat bands and a chiral lattice structure. We find by quantum-transport calculations that the chirality leads to a giant unidirectional magnetoresistance (UMR) in TBG, where the unidirectionality refers to the resistance change under the reversal of the direction of current or magnetic field. We point out that flat bands significantly enhance this effect. The UMR increases quickly upon reducing the twist angle, and reaches about 20% for an angle of 1.5° in a 10 T in-plane magnetic field. We propose the band structure topology (asymmetry), which leads to a direction-sensitive mean free path, as a useful way to anticipate the UMR effect. The UMR provides a probe for chirality and band flatness in the twisted bilayers.

Frequency Doubler and Universal Logic Gate Based on Two-Dimensional Transition Metal Dichalcogenide Transistors with Low Power Consumption

Two-dimensional transition metal dichalcogenide semiconductors are very promising candidates for future electronic applications with low power consumption due to a low leakage current and high on-off current ratio. In this study, we suggest a complementary circuit consisting of ambipolar WSe₂ and n-MoS₂ field-effect transistors (FETs), which demonstrate dual functions of a frequency doubler and single inversion AND (SAND) logic gate. In order to reduce the power consumption, a high-quality thin h-BN single crystal is used as a gate dielectric that leads to a low operating voltage of less than 5 V. By combining the low operating voltage with a low operating current in the complementary circuit, a low power consumption of 300 nW (a minimum of 10 pW) has been achieved, which is a significant improvement compared to the tens of μW consumed by a graphene channel. The complementary circuit shows the effective frequency doubling of the input with a dynamic range from 20 to 100 Hz. Furthermore, this circuit satisfies all the truth tables of a SAND logic gate that can be used as a universal logic gate like NAND. Considering that the NAND logic gate generally consists of four transistors, it is significantly advantageous to implement the equivalent circuit SAND logic gate with only two FETs. Our results open up possibilities for analog- and logic-circuit applications based on low-dimensional semiconductors.

Factors affecting the negative Poisson's ratio of black phosphorus and black arsenic: electronic effects

Negative Poisson's ratio (NPR) materials (when stretched longitudinally, the thickness of these materials increases along the lateral direction) are widely used in engineering because of their good resistance to shear, denting, and fracture. Observance of a negative Poisson's ratio (NPR) in two-dimensional (2D) single-layer materials presently has two explanations. The first, from mechanical principles, is that it derives from the presence of a special structure (hinge structure), such as in single-layer black phosphorus (BP) or black arsenic (β-As). The second, from electronic effects, is that it derives from (non-hinge-like) planar honeycomb structures and transition-metal dichalcogenides, MX2. Through first-principle calculations, we show that 2D single-layer materials with a hinge structure also have distinct electronic effects, similar to those observed from 2D planar honeycomb materials. Under strain, electronic effects of Px orbitals lead to the inherent NPR of the 2D single-layer material with a hinge structure. We discuss the influencing factors of the hinge structure on the NPR and demonstrate that the electronic effects inside the hinge structure are the fundamental factor in determining the inherent NPR.

Charge Neutral Current Generation in a Spontaneous Quantum Hall Antiferromagnet

The intrinsic Hall effect allows for the generation of a nondissipative charge neutral current, such as a pure spin current generated via the spin Hall effect. Breaking of the spatial inversion or time reversal symmetries, or the spin-orbit interaction is generally considered necessary for the generation of such a charge neutral current. Here, we challenge this general concept and present generation and detection of a charge neutral current in a centrosymmetric material with little spin-orbit interaction. We employ bilayer graphene, and find enhanced nonlocal transport in the quantum Hall antiferromagnetic state, where spontaneous symmetry breaking occurs due to the electronic correlation.

Mechanism for Anomalous Hall Ferromagnetism in Twisted Bilayer Graphene

Motivated by the recent observation of an anomalous Hall effect in twisted bilayer graphene, we use a lowest Landau level model to understand the origin of the underlying symmetry-broken correlated state. This effective model is rooted in the occurrence of Chern bands which arise due to the coupling between the graphene device and its encapsulating substrate. Our model exhibits a phase transition from a spin-valley polarized insulator to a partial or fully valley unpolarized metal as the bandwidth is increased relative to the interaction strength, consistent with experimental observations. In sharp contrast to standard quantum Hall ferromagnetism, the Chern number structure of the flat bands precludes an instability to an intervalley coherent phase, but allows for an excitonic vortex lattice at large interaction anisotropy.

Giant orbital magnetoelectric effect and current-induced magnetization switching in twisted bilayer graphene

Recently, quantum anomalous Hall effect with spontaneous ferromagnetism was observed in twisted bilayer graphenes (TBG) near 3/4 filling. Importantly, it was observed that an extremely small current can switch the direction of the magnetization. This offers the prospect of realizing low energy dissipation magnetic memories. However, the mechanism of the current-driven magnetization switching is poorly understood as the charge currents in graphenes are generally believed to be non-magnetic. In this work, we demonstrate that in TBG, the twisting and substrate induced symmetry breaking allow an out of plane orbital magnetization to be generated by a charge current. Moreover, the large Berry curvatures of the flat bands give the Bloch electrons large orbital magnetic moments so that a small current can generate a large orbital magnetization. We further demonstrate how the charge current can switch the magnetization of the ferromagnetic TBG near 3/4 filling as observed in the experiments.

The mechanism of current-driven magnetization switching in twisted bilayer graphene (TBG) is poorly understood. Here, He et al. show that a small current can generate a large orbital magnetization due to symmetry breaking by the twisting and substrate in TBG, leading to a giant orbital magnetoelectric effect.

Double Moiré with a Twist: Supermoiré in Encapsulated Graphene

A periodic spatial modulation, as created by a moiré pattern, has been extensively studied with the view to engineer and tune the properties of graphene. Graphene encapsulated by hexagonal boron nitride (hBN) when slightly misaligned with the top and bottom hBN layers experiences two interfering moiré patterns, resulting in a so-called supermoiré (SM). This leads to a lattice and electronic spectrum reconstruction. A geometrical construction of the nonrelaxed SM patterns allows us to indicate qualitatively the induced changes in the electronic properties and to locate the SM features in the density of states and in the conductivity. To emphasize the effect of lattice relaxation, we report band gaps at all Dirac-like points in the hole doped part of the reconstructed spectrum, which are expected to be enhanced when including interaction effects. Our result is able to distinguish effects due to lattice relaxation and due to the interfering SM and provides a clear picture on the origin of recently experimentally observed effects in such trilayer heterostuctures.

Superlattices based on van der Waals 2D materials

Two-dimensional (2D) materials exhibit a number of improved mechanical, optical, and electronic properties compared to their bulk counterparts. The absence of dangling bonds in the cleaved surfaces of these materials allows combining different 2D materials into van der Waals heterostructures to fabricate p-n junctions, photodetectors, and 2D-2D ohmic contacts that show unexpected performances. These intriguing results are regularly summarized in comprehensive reviews. A strategy to tailor their properties even further and to observe novel quantum phenomena consists in the fabrication of superlattices whose unit cell is formed either by two dissimilar 2D materials or by a 2D material subjected to a periodic perturbation, each component contributing with different characteristics. Furthermore, in a 2D material-based superlattice, the interlayer interaction between the layers mediated by van der Waals forces constitutes a key parameter to tune the global properties of the superlattice. The above-mentioned factors reflect the potential to devise countless combinations of van der Waals 2D material-based superlattices. In the present feature article, we explain in detail the state-of-the-art of 2D material-based superlattices and describe the different methods to fabricate them, classified as vertical stacking, intercalation with atoms or molecules, moiré patterning, strain engineering and lithographic design. We also aim to highlight some of the specific applications of each type of superlattices.

Spectroscopic studies of atomic defects and bandgap renormalization in semiconducting monolayer transition metal dichalcogenides

Assessing atomic defect states and their ramifications on the electronic properties of two-dimensional van der Waals semiconducting transition metal dichalcogenides (SC-TMDs) is the primary task to expedite multi-disciplinary efforts in the promotion of next-generation electrical and optical device applications utilizing these low-dimensional materials. Here, with electron tunneling and optical spectroscopy measurements with density functional theory, we spectroscopically locate the mid-gap states from chalcogen-atom vacancies in four representative monolayer SC-TMDs-WS2, MoS2, WSe2, and MoSe2-, and carefully analyze the similarities and dissimilarities of the atomic defects in four distinctive materials regarding the physical origins of the missing chalcogen atoms and the implications to SC-mTMD properties. In addition, we address both quasiparticle and optical energy gaps of the SC-mTMD films and find out many-body interactions significantly enlarge the quasiparticle energy gaps and excitonic binding energies, when the semiconducting monolayers are encapsulated by non-interacting hexagonal boron nitride layers.

Quasiparticle Levels at Large Interface Systems from Many-Body Perturbation Theory: The XAF-GW Method

We present a fully ab initio approach based on many-body perturbation theory in the GW approximation to compute the quasiparticle levels of large interface systems without significant covalent interactions between the different components of the interface (meaning that the different components can be separated without the creation of dangling bonds). The only assumption in our approach is that the polarizability matrix (chi) of the interface can be given by the sum of the polarizability matrices of individual components of the interface. We show analytically, using a two-state hybridized model, that this assumption is valid even in the presence of interface hybridization to form bonding and antibonding states up to first order in the overlap matrix elements involved in the hybridization. We validate our approach by showing that the band structure obtained in our method is almost identical to that obtained using a regular GW calculation for bilayer black phosphorus, where interlayer hybridization is significant. Significant savings in computational time and memory are obtained by computing chi only for the smallest subunit cell of each component and expanding (unfolding) the chi matrix to that in the unit cell of the interface. To treat interface hybridization, the full wave functions of the interface are used in computing the self-energy. We thus call the method XAF-GW (X, eXpand-chi; A, Add-chi; F, Full wave functions). Compared to GW-embedding type approaches in the literature, the XAF-GW approach is not limited to specific screening environments or to nonhybridized interface systems. XAF-GW can also be applied to systems with different dimensionalities, as well as to Moire superlattices such as in twisted bilayers. We illustrate the generality and usefulness of our approach by applying it to self-assembled PTCDA monolayers on Au(111) and Ag(111) and PTCDA monolayers on graphite-supported monolayer WSe₂. In all cases, the predicted HOMO and LUMO levels agree well with experimental measurements.