Critical size for a metal-nonmetal transition in transition-metal clusters

Abstract

Based on a tight-binding Friedel model for the density of d-electron states, we investigate the critical size for the metal-nonmetal transition in transition-metal clusters. An analytic equation for the critical size has been introduced for the cluster with close-packed structure. At the critical point (about 3050 atoms), the density of states of the cluster near the Fermi level exceeds 1/kBT and the discrete energy levels form a quasicontinuous band. The classical conducting-sphere-droplet model becomes applicable for describing the size-dependent ionization potential of those clusters larger than the critical size. Our estimation of the critical size is supported by various experimental evidence such as the threshold ionization potential, the scanning tunneling microscopy, and the core-level energy shifts. © 1994 The American Physical Society.