Control of impurity concentrations in semiconducting materials is essential to device technology. Because of their intrinsic confinement, the properties of two-dimensional semiconductors such as transition metal dichalcogenides (TMDs) are more sensitive to defects than traditional bulk materials. The technological adoption of TMDs is dependent on the mitigation of deleterious defects and guided incorporation of functional foreign atoms. The first step toward impurity control is the identification of defects and assessment of their electronic properties. Here, we present a comprehensive study of point defects in monolayer tungsten disulfide (WS 2 ) grown by chemical vapor deposition using scanning tunneling microscopy/spectroscopy, CO-tip noncontact atomic force microscopy, Kelvin probe force spectroscopy, density functional theory, and tight-binding calculations. We observe four different substitutional defects: chromium (Cr W ) and molybdenum (Mo W ) at a tungsten site, oxygen at sulfur sites in both top and bottom layers (O S top/ bottom), and two negatively charged defects (CD type I and CD type II). Their electronic fingerprints unambiguously corroborate the defect assignment and reveal the presence or absence of in-gap defect states. Cr W forms three deep unoccupied defect states, two of which arise from spin− orbit splitting. The formation of such localized trap states for Cr W differs from the Mo W case and can be explained by their different d shell energetics and local strain, which we directly measured. Utilizing a tight-binding model the electronic spectra of the isolectronic substitutions O S and Cr W are mimicked in the limit of a zero hopping term and infinite on-site energy at a S and W site, respectively. The abundant CDs are negatively charged, which leads to a significant band bending around the defect and a local increase of the contact potential difference. In addition, CD-rich domains larger than 100 nm are observed, causing a work function increase of 1.1 V. While most defects are electronically isolated, we also observed hybrid states formed between Cr W dimers. The important role of charge localization, spin−orbit coupling, and strain for the formation of deep defect states observed at substitutional defects in WS 2 as reported here will guide future efforts of targeted defect engineering and doping of TMDs.

Recent progress in the design and fabrication of artificial two-dimensional (2D) materials paves the way for the experimental realization of electron systems moving on complex geometries, such as plane fractals. In this work, we calculate the quantum conductance of a 2D electron gas roaming on a Sierpinski carpet (SC), i.e., a plane fractal with Hausdorff dimension intermediate between 1 and 2. We find that the fluctuations of the quantum conductance are a function of energy with a fractal graph, whose dimension can be chosen by changing the geometry of the SC. This behavior is independent of the underlying lattice geometry.

We study the quantum Hall effect of 2D electron gas in black phosphorus in the presence of perpendicular electric and magnetic fields. In the absence of a bias voltage, the external magnetic field leads to a quantization of the energy spectrum into equidistant Landau levels, with different cyclotron frequencies for the electron and hole bands. The applied voltage reduces the band gap, and eventually a semiconductor to semimetal transition takes place. This nontrivial phase is characterized by the emergence of a pair of Dirac points in the spectrum. As a consequence, the Landau levels are not equidistant anymore, but follow the εn ∝ √ nB characteristic of Dirac crystals as graphene. By using the Kubo-Bastin formula in the context of the kernel polynomial method, we compute the Hall conductivity of the system. We obtain a σxy ∝ 2n quantization of the Hall conductivity in the gapped phase (standard quantum Hall effect regime), and a σxy ∝ 4(n + 1/2) quantization in the semimetalic phase, characteristic of Dirac systems with non-trivial topology.

A properly strained graphene monolayer or bilayer is expected to harbour periodic pseudo-magnetic fields with high symmetry, yet to date, a convincing demonstration of such pseudo-magnetic fields has been lacking, especially for bilayer graphene. Here, we report the first definitive experimental proof for the existence of large-area, periodic pseudo-magnetic fields, as manifested by vortex lattices in commensurability with the moiré patterns of low-angle twisted bilayer graphene. The pseudo-magnetic fields are strong enough to confine the massive Dirac electrons into circularly localized pseudo-Landau levels, as observed by scanning tunneling microscopy/spectroscopy, and also corroborated by tight-binding calculations. We further demonstrate that the geometry, amplitude, and periodicity of the pseudo-magnetic field can be fine-tuned by both the rotation angle and heterostrain applied to the system. Collectively, the present study substantially enriches twisted bilayer graphene as a powerful enabling platform for exploration of new and exotic physical phenomena, including quantum valley Hall effects and quantum anomalous Hall effects.

Recent progress in the fabrication of materials has made it possible to create arbitrary non-periodic two-dimensional structures in the quantum plasmon regime. This paves the way for exploring the plasmonic properties of electron gases in complex geometries such as fractals. In this work, we study the plasmonic properties of Sierpinski carpets and gaskets, two prototypical fractals with different ramification, by fully calculating their dielectric functions. We show that the Sierpinski carpet has a dispersion comparable to a square lattice, but the Sierpinski gasket features highly localized plasmon modes with a flat dispersion. This strong plasmon confinement in finitely ramified fractals can provide a novel setting for manipulating light at the quantum scale.