Direct Evidence of Klein and Anti-Klein Tunneling of Graphitic Electrons in a Corbino Geometry.

Transport measurement of electron optics in monolayer graphene p-n junction devices has been traditionally studied with negative refraction and chiral transmission experiments in Hall bar magnetic focusing setups. We show direct signatures of Klein (monolayer) and anti-Klein (bilayer) tunneling with a circular "edgeless" Corbino geometry made out of gated graphene p-n junctions. Noticeable in particular is the appearance of angular sweet spots (Brewster angles) in the magnetoconductance data of bilayer graphene, which minimizes head-on transmission, contrary to conventional Fresnel optics or monolayer graphene which show instead a sharpened collimation of transmission paths. The local maxima on the bilayer magnetoconductance plots migrate to higher fields with increasing doping density. These experimental results are in good agreement with detailed numerical simulations and analytical predictions.

Evidence of the fractional quantum spin Hall effect in moiré MoTe2.

Quantum spin Hall (QSH) insulators are two-dimensional electronic materials that have a bulk band gap similar to an ordinary insulator but have topologically protected pairs of edge modes of opposite chiralities1-6. So far, experimental studies have found only integer QSH insulators with counter-propagating up-spins and down-spins at each edge leading to a quantized conductance G0 = e2/h (with e and h denoting the electron charge and Planck's constant, respectively)7-14. Here we report transport evidence of a fractional QSH insulator in 2.1° twisted bilayer MoTe2, which supports spin-Sz conservation and flat spin-contrasting Chern bands15,16. At filling factor ν = 3 of the moiré valence bands, each edge contributes a conductance 3 2 G 0 with zero anomalous Hall conductivity. The state is probably a time-reversal pair of the even-denominator 3/2-fractional Chern insulators. Furthermore, at ν = 2, 4 and 6, we observe a single, double and triple QSH insulator with each edge contributing a conductance G0, 2G0 and 3G0, respectively. Our results open up the possibility of realizing time-reversal symmetric non-abelian anyons and other unexpected topological phases in highly tunable moiré materials17-19.

Thermodynamic evidence of fractional Chern insulator in moiré MoTe2.

Chern insulators, which are the lattice analogues of the quantum Hall states, can potentially manifest high-temperature topological orders at zero magnetic field to enable next-generation topological quantum devices1-3. Until now, integer Chern insulators have been experimentally demonstrated in several systems at zero magnetic field3-8, whereas fractional Chern insulators have been reported in only graphene-based systems under a finite magnetic field9,10. The emergence of semiconductor moiré materials11, which support tunable topological flat bands12,13, provides an opportunity to realize fractional Chern insulators13-16. Here we report thermodynamic evidence of both integer and fractional Chern insulators at zero magnetic field in small-angle twisted bilayer MoTe2 by combining the local electronic compressibility and magneto-optical measurements. At hole filling factor ν = 1 and 2/3, the system is incompressible and spontaneously breaks time-reversal symmetry. We show that they are integer and fractional Chern insulators, respectively, from the dispersion of the state in the filling factor with an applied magnetic field. We further demonstrate electric-field-tuned topological phase transitions involving the Chern insulators. Our findings pave the way for the demonstration of quantized fractional Hall conductance and anyonic excitation and braiding17 in semiconductor moiré materials.

Switchable moiré potentials in ferroelectric WTe2/WSe2 superlattices.

Moiré materials with superlattice periodicity many times the atomic length scale have shown strong electronic correlations and band topology with unprecedented tunability. Non-volatile control of the moiré potentials could allow on-demand switching of superlattice effects but has remained challenging to achieve. Here we demonstrate the switching of the correlated and moiré band insulating states, and the associated nonlinear anomalous Hall effect, by the ferroelectric effect. This is achieved in a ferroelectric WTe2 bilayer of the Td structure with a centred-rectangular moiré superlattice induced by interfacing with a WSe2 monolayer of the H structure. The results can be understood in terms of polarization-dependent charge transfer between two WTe2 monolayers, in which the interfacial layer has a much stronger moiré potential depth; ferroelectric switching thus turns on and off the moiré insulating states. Our study demonstrates the potential for creating new functional moiré materials by incorporating intrinsic symmetry-breaking orders.

Exciton density waves in Coulomb-coupled dual moiré lattices.

Strongly correlated bosons in a lattice are a platform that can realize rich bosonic states of matter and quantum phase transitions1. While strongly correlated bosons in a lattice have been studied in cold-atom experiments2-4, their realization in a solid-state system has remained challenging5. Here we trap interlayer excitons-bosons composed of bound electron-hole pairs, in a lattice provided by an angle-aligned WS2/bilayer WSe2/WS2 multilayer. The heterostructure supports Coulomb-coupled triangular moiré lattices of nearly identical period at the top and bottom interfaces. We observe correlated insulating states when the combined electron filling factor of the two lattices, with arbitrary partitions, equals [Formula: see text] and [Formula: see text]. These states can be interpreted as exciton density waves in a Bose-Fermi mixture of excitons and holes6,7. Because of the strong repulsive interactions between the constituents, the holes form robust generalized Wigner crystals8-11, which restrict the exciton fluid to channels that spontaneously break the translational symmetry of the lattice. Our results demonstrate that Coulomb-coupled moiré lattices are fertile ground for correlated many-boson phenomena12,13.

Electrical conductivity in a non-covalent two-dimensional porous organic material with high crystallinity.

Electroactive macrocycle building blocks are a promising route to new types of functional two-dimensional porous organic frameworks. Our strategy uses conjugated macrocycles that organize into two dimensional porous sheets via non-covalent van der Waals interactions, to make ultrathin films that are just one molecule thick. In bulk, these two-dimensional (2D) sheets stack into a three-dimensional van der Waals crystal, where relatively weak alkyl-alkyl interactions constitute the interface between these sheets. With the liquid-phase exfoliation, we are able to obtain films as thin as two molecular layers. Further using a combination of liquid-phase and mechanical exfoliation, we are able to create non-covalent sheets over a large area (>100 µm2). The ultrathin porous films maintain the single crystal packing from the macrocyclic structure and are electrically conductive. We demonstrate that this new type of 2D non-covalent porous organic framework can be used as the active layer in a field effect transistor device with graphene source and drain contacts along with hexagonal boron nitride as the gate dielectric interface.

Edge channels of broken-symmetry quantum Hall states in graphene visualized by atomic force microscopy.

The quantum Hall (QH) effect, a topologically non-trivial quantum phase, expanded the concept of topological order in physics bringing into focus the intimate relation between the "bulk" topology and the edge states. The QH effect in graphene is distinguished by its four-fold degenerate zero energy Landau level (zLL), where the symmetry is broken by electron interactions on top of lattice-scale potentials. However, the broken-symmetry edge states have eluded spatial measurements. In this article, we spatially map the quantum Hall broken-symmetry edge states comprising the graphene zLL at integer filling factors of [Formula: see text] across the quantum Hall edge boundary using high-resolution atomic force microscopy (AFM) and show a gapped ground state proceeding from the bulk through to the QH edge boundary. Measurements of the chemical potential resolve the energies of the four-fold degenerate zLL as a function of magnetic field and show the interplay of the moiré superlattice potential of the graphene/boron nitride system and spin/valley symmetry-breaking effects in large magnetic fields.

Visualization of moiré superlattices.

Moiré superlattices in van der Waals heterostructures have given rise to a number of emergent electronic phenomena due to the interplay between atomic structure and electron correlations. Indeed, electrons in these structures have been recently found to exhibit a number of emergent properties that the individual layers themselves do not exhibit. This includes superconductivity1,2, magnetism3, topological edge states4,5, exciton trapping6 and correlated insulator phases7. However, the lack of a straightforward technique to characterize the local structure of moiré superlattices has thus far impeded progress in the field. In this work we describe a simple, room-temperature, ambient method to visualize real-space moiré superlattices with sub-5-nm spatial resolution in a variety of twisted van der Waals heterostructures including, but not limited to, conducting graphene, insulating boron nitride and semiconducting transition metal dichalcogenides. Our method uses piezoresponse force microscopy, an atomic force microscope modality that locally measures electromechanical surface deformation. We find that all moiré superlattices, regardless of whether the constituent layers have inversion symmetry, exhibit a mechanical response to out-of-plane electric fields. This response is closely tied to flexoelectricity wherein electric polarization and electromechanical response is induced through strain gradients present within moiré superlattices. Therefore, moiré superlattices of two-dimensional materials manifest themselves as an interlinked network of polarized domain walls in a non-polar background matrix.

High-Quality Electrostatically Defined Hall Bars in Monolayer Graphene.

Realizing graphene's promise as an atomically thin and tunable platform for fundamental studies and future applications in quantum transport requires the ability to electrostatically define the geometry of the structure and control the carrier concentration, without compromising the quality of the system. Here, we demonstrate the working principle of a new generation of high-quality gate-defined graphene samples, where the challenge of doing so in a gapless semiconductor is overcome by using the ν = 0 insulating state, which emerges at modest applied magnetic fields. In order to verify that the quality of our devices is not compromised, we compare the electronic transport response of different sample geometries, paying close attention to fragile quantum states, such as the fractional quantum Hall states that are highly susceptible to disorder. The ability to define local depletion regions without compromising device quality establishes a new approach toward structuring graphene-based quantum transport devices.

Quantitative analysis of 17 amino acids in tobacco leaves using an amino acid analyzer and chemometric resolution.

A method was developed for quantifying 17 amino acids in tobacco leaves by using an A300 amino acid analyzer and chemometric resolution. In the method, amino acids were eluted by the buffer solution on an ion-exchange column. After reacting with ninhydrin, the derivatives of amino acids were detected by ultraviolet detection. Most amino acids are separated by the elution program. However, five peaks of the derivatives are still overlapping. A non-negative immune algorithm was employed to extract the profiles of the derivatives from the overlapping signals, and then peak areas were adopted for quantitative analysis of the amino acids. The method was validated by the determination of amino acids in tobacco leaves. The relative standard deviations (n = 5) are all less than 2.54% and the recoveries of the spiked samples are in a range of 94.62-108.21%. The feasibility of the method was proved by analyzing the 17 amino acids in 30 tobacco leaf samples.

Step-by-step fracture of two-layer stacked graphene membranes.

Layer-by-layer assembly of graphene has been proven to be an effective way to improve its mechanical properties, but its fracture mechanism, which is crucial for practical device applications, is still not clear and has not been fully studied yet. By consecutive stacking of two graphene monolayers, we fabricate two-layer stacked graphene membranes with a clean interface between the two layers. Fracture behavior of the two-layer stacked graphene membranes is studied using nanoindentation performed by atomic force microscopy. It is found that the fracture force distribution of stacked graphene is very different from that of monolayer graphene. Weibull statistics of fracture forces show that after layer-by-layer stacking of graphene, the membrane becomes less sensitive to the defects during nanoindentation, improving the overall performance of the graphene membranes. Interestingly, a third of our tested membranes show a stepwise fracture, which could serve as a warning message for the mechanical failure of multilayer graphene devices. Our study provides insight into the fracture mechanism of multilayer graphene membranes.