W mass in a model with vectorlike leptons and U ( 1 ) ′
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Monolayer transition-metal dichalcogenides (TMDCs) have been extensively studied due to their wide range of physical properties and applications. It has been demonstrated that the electron beam in a transmission electron microscope (TEM) or scanning TEM (STEM) generates chalcogen vacancies that agglomerate into dispersed linelike or holelike defects. Here we employ a STEM electron beam and demonstrate that, in WSe 2 , beam-induced chalcogen vacancies initially form certain dispersed multivacancy structures, as seen in TMDCs in prior work. However, with suitable control of the STEM focused electron beam, these multivacancies gradually evolve into a dense network of ten-, 12-, 14-, and 16-member ring round holes, whereas the same process leads predominantly to chalcogen-vacancy line defects in other trigonal-prismatic TMDCs. Density functional theory calculations find that the underlying atomic-scale processes lead preferentially to defect structures that lower the total energy so that we are able to track the formation of the observed multivacancy complexes, which then lead to the formation of dense large round holes in WSe 2 . The same processes in WS 2 , however, are energetically unfavorable, while linear multivacancy defects are preferred, as observed. The demonstrated control of the formation of unique high-density round holes in WSe 2 has potential for applications such as atomic and molecular sieving.
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The quasiparticle self-consistent 𝐺𝑊 method is used to study the electronic band structure, optical dielectric function, and exchange interactions in chalcopyrite, 𝐼 ‾ 4 2𝑑, structure MnGeP 2 . The material is found to be an antiferromagnetic semiconductor with a lowest direct gap of 2.44 eV at the Γ point and a lower indirect gap of 1.87 eV from Γ to 𝑀. The material is an altermagnet because the two magnetic atoms of opposite spin are related by a twofold rotation operation perpendicular to the main fourfold rotation inversion axis. The spin splittings along a low symmetry line like 𝑃𝑁 is sizable while at k points on the diagonal mirror planes or on the twofold symmetry axes the spin splitting is zero. The exchange interactions are calculated using a linear response approach. The antiferromagnetic exchange interaction between nearest neighbors in the primitive unit cell is dominating and found to be slightly decreasing upon carrier doping but not sufficiently to change the interaction to become ferromagnetic. The bare (noninteracting) and interacting transverse spin susceptibilities, which provide interatomic site exchange interactions after averaging over the muffin-tin spheres, are calculated from the 𝐺𝑊 band structure and wave functions. From these exchange interactions, the spin wave spectra are obtained along the high symmetry lines and the Néel temperature is calculated using the mean-field and Tyablikov estimations. The dielectric function and the optical absorption spectra are calculated including excitonic effects using the Bethe Salpeter equation. The exchange interactions around Mn Ge defect sites is also studied. While we find it can generate ferromagnetic interactions with neighboring spins, we did not find direct evidence of producing an overall ferromagnetic phase. First, if Mn antisites are introduced by exchanging Mn with a nearby Ge, the interactions stay largely antiferromagnetic. Second, when we add additional Mn, in other words in Mn-rich stoichiometry, the Mn Ge antisites produce a strong ferromagnetic interaction primarily with the Mn in the same basal plane but weaker ferromagnetic interaction with adjacent plane Mn. The interactions between regular lattice Mn stay antiferromagnetic as before and thus favor keeping the antiferromagnetic order along the [001] direction. Adding Mn antisites, however, does lead to a metallic band structure.
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