Anomalous minimum and scaling behavior of localization length near an isolated flat band

Using one-dimensional tight-binding lattices and an analytical expression based on the Green's matrix, we show that anomalous minimum of the localization length near an isolated flat band, previously found for evanescent waves in a defect-free photonic crystal waveguide, is a generic feature and exists in the Anderson regime as well, i.e., in the presence of disorder. Our finding reveals a scaling behavior of the localization length in terms of the disorder strength, as well as a summation rule of the inverse localization length in terms of the density of states in different bands. Most interesting, the latter indicates the possibility of having two localization minima inside a band gap, if this band gap is formed by two flat bands such as in a double-sided Lieb lattice.Comment: 8 pages, 9 figure

Highly selective electrochemical hydrogenation of alkynes: Rapid construction of mechanochromic materials

Electrochemical hydrogenation has emerged as an environmentally benign and operationally simple alternative to traditional catalytic reduction of organic compounds. Here, we have disclosed for the first time the electrochemical hydrogenation of alkynes to a library of synthetically important Z-alkenes under mild conditions with great selectivity and efficiency. The deuterium and control experiments of electrochemical hydrogenation suggest that the hydrogen source comes from the solvent, supporting electrolyte, and base. The scanning electron microscopy and x-ray diffraction experiments demonstrate that palladium nanoparticles generated in the electrochemical reaction act as a chemisorbed hydrogen carrier. Moreover, complete reduction of alkynes to saturated alkanes can be achieved through slightly modified conditions. Furthermore, a series of novel mechanofluorochromic materials have been efficiently constructed with this protocol that showed blue-shifted mechanochromism. This discovery represents the first example of cis-olefins-based organic mechanochromic materials