Optical anisotropy is one of the most fundamental physical characteristics of emerging low-symmetry two-dimensional (2D) materials. It provides abundant structural information and is crucial for creating diverse nanoscale devices. Here, we have proposed an azimuth-resolved microscopic approach to directly resolve the normalized optical difference along two orthogonal directions at normal incidence. The differential principle ensures that the approach is only sensitive to anisotropic samples and immune to isotropic materials. We studied the optical anisotropy of bare and encapsulated black phosphorus (BP) and unveiled the interference effect on optical anisotropy, which is critical for practical applications in optical and optoelectronic devices. A multi-phase model based on the scattering matrix method was developed to account for the interference effect and then the crystallographic directions were unambiguously determined. Our result also suggests that the optical anisotropy is a probe to measure the thickness with monolayer resolution. Furthermore, the optical anisotropy of rhenium disulfide (ReS2), another class of anisotropic 2D materials, with a 1T distorted crystal structure, was investigated, which demonstrates that our approach is suitable for other anisotropic 2D materials. This technique is ideal for optical anisotropy characterization and will inspire future efforts in BP and related anisotropic 2D nanomaterials for engineering new conceptual nanodevices.

Two-step rapid thermal thinning obtains monolayer black phosphorus with a high surface quality.

Clustering validation has long been recognized as one of the vital issues essential to the success of clustering applications. In general, clustering validation can be categorized into two classes, external clustering validation and internal clustering validation. In this paper, we focus on internal clustering validation and present a study of 11 widely used internal clustering validation measures for crisp clustering. The results of this study indicate that these existing measures have certain limitations in different application scenarios. As an alternative choice, we propose a new internal clustering validation measure, named clustering validation index based on nearest neighbors (CVNN), which is based on the notion of nearest neighbors. This measure can dynamically select multiple objects as representatives for different clusters in different situations. Experimental results show that CVNN outperforms the existing measures on both synthetic data and real-world data in different application scenarios.

Layered black phosphorus (BP) has been expected to be a promising material for future electronic and optoelectronic applications since its discovery. However, the difficulty in mass fabricating layered air-stable BP severely obstructs its potential industry applications. Here, we report a new BP chemical modification method to implement all-solution-based mass production of layered air-stable BP. This method uses the combination of two electron-deficient reagents 2,2,6,6-tetramethylpiperidinyl-N-oxyl (TEMPO) and triphenylcarbenium tetrafluorobor ([Ph3C]­BF4) to accomplish thinning and/or passivation of BP in organic solvent. The field-effect transistor and photodetection devices constructed from the chemically modified BP flakes exhibit enhanced performances with environmental stability up to 4 months. A proof-of-concept BP thin-film transistor fabricated through the all-solution-based exfoliation and modification displays an air-stable and a typical p-type transistor behavior. This all-solution-based method improves the prospects of BP for industry applications.

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