Kondo Effect in Fermi Systems with a Gap: A Renormalization Group Study

We present the results of a Wilson Renormalization Group study of the single-impurity Kondo and Anderson models in a system with a gap in the conduction electron spectrum. The behavior of the impurity susceptibility and the zero-frequency response function, $T>$ are discussed in the cases with and without particle-hole symmetry. In addition, for the asymmetric Anderson model the correlation functions, $<\vec S \cdot\vec \sigma (0)>$,$$, and$$ are computed.Comment: 10 pages, 10 figure

In Situ Thermal Decomposition of Exfoliated Two-Dimensional Black Phosphorus

With a semiconducting band gap and high charge carrier mobility, two-dimensional (2D) black phosphorus (BP), often referred to as phosphorene, holds significant promise for next generation electronics and optoelectronics. However, as a 2D material, it possesses a higher surface area to volume ratio than bulk BP, suggesting that its chemical and thermal stability will be modified. Herein, an atomic-scale microscopic and spectroscopic study is performed to characterize the thermal degradation of mechanically exfoliated 2D BP. From in situ scanning/transmission electron microscopy, decomposition of 2D BP is observed to occur at ~400 {\deg}C in vacuum, in contrast to the 550 {\deg}C bulk BP sublimation temperature. This decomposition initiates via eye-shaped cracks along the [001] direction and then continues until only a thin, amorphous red phosphorous like skeleton remains. In situ electron energy loss spectroscopy, energy-dispersive X-ray spectroscopy, and energy-loss near-edge structure changes provide quantitative insight into this chemical transformation process.Comment: In press: 4 figures in main manuscript, 27 pages with supporting informatio