Localized States of a Binary Alloy

摘要: The localization phenomena exhibited by a commonly studied model of electrons in substitutional alloy are found to be much richer than has previously been reported. A nondegenerate tight-binding band arising primarily from one constituent the is considered. It may possess states localized small isolated clusters (as percolation theory), and decaying exponentially at large distances Anderson model), plus third class which have not discussed before. These last occur special energies, but bulk material. Examples constructed, an approximate calculation their spectral weight carried out. This enumeration provides explanation anomalies appeared recent numerical calculations density this model. continuous part spectrum also displays surprising behavior, as revealed calculations. There appears "forbidden energy" center band, goes continuously zero. eigenstates nearby energies appear sense. exhibits one, several pairs mobility edges, separating extended states. make available nontrivial exact results for three-dimensional disordered material, test theories. None existing theories predict these effects. In addition, we suggest real systems new states, perhaps associated effects on spectrum, can observed.