Twistable electronics with dynamically rotatable heterostructures

In heterostructures of two-dimensional materials, electronic properties can vary dramatically with relative interlayer angle. This effect makes it theoretically possible to realize a new class of twistable electronics in which properties can be manipulated on demand by means of rotation. We demonstrate a device architecture in which a layered heterostructure can be dynamically twisted in situ. We study graphene encapsulated by boron nitride, where, at small rotation angles, the device characteristics are dominated by coupling to a long-wavelength moiré superlattice. The ability to investigate arbitrary rotation angle in a single device reveals features of the optical, mechanical, and electronic response in this system not captured in static rotation studies. Our results establish the capability to fabricate twistable electronic devices with dynamically tunable properties.

Compression-Induced Modification of Boron Nitride Layers: A Conductive Two-Dimensional BN Compound

The ability to create materials with improved properties upon transformation processes applied to conventional materials is the keystone of materials science. Here, hexagonal boron nitride (h-BN), a large-band-gap insulator, is transformed into a conductive two-dimensional (2D) material- bonitrol-that is stable at ambient conditions. The process, which requires compression of at least two h-BN layers and hydroxyl ions, is characterized via scanning probe microscopy experiments and ab initio calculations. This material and its creation mechanism represent an additional strategy for the transformation of known 2D materials into artificial advanced materials with exceptional properties.

Interfacial engineering in graphene bandgap

Graphene exhibits superior mechanical strength, high thermal conductivity, strong light-matter interactions, and, in particular, exceptional electronic properties. These merits make graphene an outstanding material for numerous potential applications. However, a graphene-based high-performance transistor, which is the most appealing application, has not yet been produced, which is mainly due to the absence of an intrinsic electronic bandgap in this material. Therefore, bandgap opening in graphene is urgently needed, and great efforts have been made regarding this topic over the past decade. In this review article, we summarise recent theoretical and experimental advances in interfacial engineering to achieve bandgap opening. These developments are divided into two categories: chemical engineering and physical engineering. Chemical engineering is usually destructive to the pristine graphene lattice via chemical functionalization, the introduction of defects, doping, chemical bonds with substrates, and quantum confinement; the latter largely maintains the atomic structure of graphene intact and includes the application of an external field, interactions with substrates, physical adsorption, strain, electron many-body effects and spin-orbit coupling. Although these pioneering works have not met all the requirements for electronic applications of graphene at once, they hold great promise in this direction and may eventually lead to future applications of graphene in semiconductor electronics and beyond.

High-order fractal states in graphene superlattices

Graphene superlattices were shown to exhibit high-temperature quantum oscillations due to periodic emergence of delocalized Bloch states in high magnetic fields such that unit fractions of the flux quantum pierce a superlattice unit cell. Under these conditions, semiclassical electron trajectories become straight again, similar to the case of zero magnetic field. Here, we report magnetotransport measurements that reveal second-, third-, and fourth-order magnetic Bloch states at high electron densities and temperatures above 100 K. The recurrence of these states creates a fractal pattern intimately related to the origin of Hofstadter butterflies. The hierarchy of the fractal states is determined by the width of magnetic minibands, in qualitative agreement with our band-structure calculations.

Observation of fractional Chern insulators in a van der Waals heterostructure

Topologically ordered phases are characterized by long-range quantum entanglement and fractional statistics rather than by symmetry breaking. First observed in a fractionally filled continuum Landau level, topological order has since been proposed to arise more generally at fractional fillings of topologically nontrivial Chern bands. Here we report the observation of gapped states at fractional fillings of Harper-Hofstadter bands arising from the interplay of a magnetic field and a superlattice potential in a bilayer graphene-hexagonal boron nitride heterostructure. We observed phases at fractional filling of bands with Chern indices [Formula: see text] Some of these phases, in [Formula: see text] and [Formula: see text] bands, are characterized by fractional Hall conductance-that is, they are known as fractional Chern insulators and constitute an example of topological order beyond Landau levels.

Integer and Fractional Quantum Hall effect in Ultrahigh Quality Few-layer Black Phosphorus Transistors

As a high mobility two-dimensional semiconductor with strong structural and electronic anisotropy, atomically thin black phosphorus (BP) provides a new playground for investigating the quantum Hall (QH) effect, including outstanding questions such as the functional dependence of Landau level (LL) gaps on magnetic field B, and possible anisotropic fractional QH states. Using encapsulated few-layer BP transistors with mobility up to 55 000 cm²/(V s), we extracted LL gaps over an exceptionally wide range of B for QH states at filling factors -1 to -4, which are determined to be linear in B, thus resolving a controversy raised by its anisotropy. Furthermore, a fractional QH state at ν ≈ -4/3 and an additional feature at -0.56 ± 0.1 are observed, underscoring BP as a tunable 2D platform for exploring electron interactions.

High-temperature quantum oscillations caused by recurring Bloch states in graphene superlattices

Cyclotron motion of charge carriers in metals and semiconductors leads to Landau quantization and magneto-oscillatory behavior in their properties. Cryogenic temperatures are usually required to observe these oscillations. We show that graphene superlattices support a different type of quantum oscillation that does not rely on Landau quantization. The oscillations are extremely robust and persist well above room temperature in magnetic fields of only a few tesla. We attribute this phenomenon to repetitive changes in the electronic structure of superlattices such that charge carriers experience effectively no magnetic field at simple fractions of the flux quantum per superlattice unit cell. Our work hints at unexplored physics in Hofstadter butterfly systems at high temperatures.

van der Waals Layered Materials: Opportunities and Challenges

Since graphene became available by a scotch tape technique, a vast class of two-dimensional (2D) van der Waals (vdW) layered materials has been researched intensively. What is more intriguing is that the well-known physics and chemistry of three-dimensional (3D) bulk materials are often irrelevant, revealing exotic phenomena in 2D vdW materials. By further constructing heterostructures of these materials in the planar and vertical directions, which can be easily achieved via simple exfoliation techniques, numerous quantum mechanical devices have been demonstrated for fundamental research and technological applications. It is, therefore, necessary to review the special features in 2D vdW materials and to discuss the remaining issues and challenges. Here, we review the vdW materials library, technology relevance, and specialties of vdW materials covering the vdW interaction, strong Coulomb interaction, layer dependence, dielectric screening engineering, work function modulation, phase engineering, heterostructures, stability, growth issues, and the remaining challenges.

Emergence of Tertiary Dirac Points in Graphene Moiré Superlattices

The electronic structure of a crystalline solid is largely determined by its lattice structure. Recent advances in van der Waals solids, artificial crystals with controlled stacking of two-dimensional (2D) atomic films, have enabled the creation of materials with novel electronic structures. In particular, stacking graphene on hexagonal boron nitride (hBN) introduces a moiré superlattice that fundamentally modifies graphene's band structure and gives rise to secondary Dirac points (SDPs). Here we find that the formation of a moiré superlattice in graphene on hBN yields new, unexpected consequences: a set of tertiary Dirac points (TDPs) emerge, which give rise to additional sets of Landau levels when the sample is subjected to an external magnetic field. Our observations hint at the formation of a hidden Kekulé superstructure on top of the moiré superlattice under appropriate carrier doping and magnetic fields.

Periodic potentials in hybrid van der Waals heterostructures formed by supramolecular lattices on graphene

The rise of 2D materials made it possible to form heterostructures held together by weak interplanar van der Waals interactions. Within such van der Waals heterostructures, the occurrence of 2D periodic potentials significantly modifies the electronic structure of single sheets within the stack, therefore modulating the material properties. However, these periodic potentials are determined by the mechanical alignment of adjacent 2D materials, which is cumbersome and time-consuming. Here we show that programmable 1D periodic potentials extending over areas exceeding 104 nm2 and stable at ambient conditions arise when graphene is covered by a self-assembled supramolecular lattice. The amplitude and sign of the potential can be modified without altering its periodicity by employing photoreactive molecules or their reaction products. In this regard, the supramolecular lattice/graphene bilayer represents the hybrid analogue of fully inorganic van der Waals heterostructures, highlighting the rich prospects that molecular design offers to create ad hoc materials.

Fabry-Pérot Resonances in a Graphene/hBN Moiré Superlattice

While Fabry-Pérot (FP) resonances and Moiré superlattices are intensively studied in graphene on hexagonal boron nitride (hBN), the two effects have not been discussed in their coexistence. Here we investigate the FP oscillations in a ballistic pnp-junctions in the presence and absence of a Moiré superlattice. First, we address the effect of the smoothness of the confining potential on the visibility of the FP resonances and carefully map the evolution of the FP cavity size as a function of densities inside and outside the cavity in the absence of a superlattice, when the cavity is bound by regular pn-junctions. Using a sample with a Moiré superlattice, we next show that an FP cavity can also be formed by interfaces that mimic a pn-junction but are defined through a satellite Dirac point due to the superlattice. We carefully analyze the FP resonances, which can provide insight into the band-reconstruction due to the superlattice.

Electronic structure of transferred graphene/h-BN van der Waals heterostructures with nonzero stacking angles by nano-ARPES

In van der Waals heterostructures, the periodic potential from the Moiré superlattice can be used as a control knob to modulate the electronic structure of the constituent materials. Here we present a nanoscale angle-resolved photoemission spectroscopy (nano-ARPES) study of transferred graphene/h-BN heterostructures with two different stacking angles of 2.4° and 4.3° respectively. Our measurements reveal six replicas of graphene Dirac cones at the superlattice Brillouin zone (SBZ) centers. The size of the SBZ and its relative rotation angle to the graphene BZ are in good agreement with Moiré superlattice period extracted from atomic force microscopy (AFM) measurements. Comparison to the epitaxial graphene/h-BN with 0° stacking angles suggests that the interaction between graphene and h-BN decreases with increasing stacking angle.

Fractional Hofstadter States in Graphene on Hexagonal Boron Nitride

In fractionally filled Landau levels there is only a small energy difference between broken translational symmetry electron-crystal states and exotic correlated quantum fluid states. We show that the spatially periodic substrate interaction associated with the long period moiré patterns present in graphene on nearly aligned hexagonal boron nitride tilts this close competition in favor of the former, explaining surprising recent experimental findings.

The hot pick-up technique for batch assembly of van der Waals heterostructures

The assembly of individual two-dimensional materials into van der Waals heterostructures enables the construction of layered three-dimensional materials with desirable electronic and optical properties. A core problem in the fabrication of these structures is the formation of clean interfaces between the individual two-dimensional materials which would affect device performance. We present here a technique for the rapid batch fabrication of van der Waals heterostructures, demonstrated by the controlled production of 22 mono-, bi- and trilayer graphene stacks encapsulated in hexagonal boron nitride with close to 100% yield. For the monolayer devices, we found semiclassical mean-free paths up to 0.9 μm, with the narrowest samples showing clear indications of the transport being affected by boundary scattering. The presented method readily lends itself to fabrication of van der Waals heterostructures in both ambient and controlled atmospheres, while the ability to assemble pre-patterned layers paves the way for complex three-dimensional architectures.

The reliable assembly of two-dimensional materials into van der Waals heterostructures is a critical step towards nanoscale electronic integration. Here the authors present a technique for batch fabrication of graphene/boron nitride stacks with clean interfaces and high-yield.

Hofstadter Butterfly and Many-Body Effects in Epitaxial Graphene Superlattice

Graphene placed on hexagonal boron nitride (h-BN) has received a wide range of interest due to the improved electrical performance and rich physics from the interface, especially the emergence of superlattice Dirac points as well as Hofstadter butterfly in high magnetic field. Instead of transferring graphene onto h-BN, epitaxial growth of graphene directly on a single-crystal h-BN provides an alternative and promising way to study these interesting superlattice effects due to their precise lattice alignment. Here we report an electrical transport study on epitaxial graphene superlattice on h-BN with a period of ∼15.6 nm. The epitaxial graphene superlattice is clean, intrinsic, and of high quality with a carrier mobility of ∼27 000 cm(2) V(-1) s(-1), which enables the observation of Hofstadter butterfly features originated from the superlattice at a magnetic field as low as 6.4 T. A metal-insulator transition and magnetic field dependent Fermi velocity were also observed, suggesting prominent electron-electron interaction-induced many-body effects.

Macroscopic self-reorientation of interacting two-dimensional crystals

Microelectromechanical systems, which can be moved or rotated with nanometre precision, already find applications in such fields as radio-frequency electronics, micro-attenuators, sensors and many others. Especially interesting are those which allow fine control over the motion on the atomic scale because of self-alignment mechanisms and forces acting on the atomic level. Such machines can produce well-controlled movements as a reaction to small changes of the external parameters. Here we demonstrate that, for the system of graphene on hexagonal boron nitride, the interplay between the van der Waals and elastic energies results in graphene mechanically self-rotating towards the hexagonal boron nitride crystallographic directions. Such rotation is macroscopic (for graphene flakes of tens of micrometres the tangential movement can be on hundreds of nanometres) and can be used for reproducible manufacturing of aligned van der Waals heterostructures.