On Mesoscopic Forces and Quantized Conductance in Model Metallic Nanowires

Identification and understanding of the physical origins and systematics underlying the variations of material properties with size, form of aggregation, and dimensionality are some of the main challenges in modern materials research, of ever increasing importance in the face of the accelerated trend toward miniaturization of electronic and mechanical devices. While for over two decades studies of size-evolutionary patterns of materials have focused on atomic and molecular clusters 1-3 in beams or embedded in inert matrices, more recent efforts concentrated on preparation, characterization, and understanding of finite solid-state structures. These include nanometer-scale metal and semiconductor nanocrystals, 4-6 surface-supported structures and quantum dots, 7 and nanoscale junctions or wires. 8-27 Interestingly, it has emerged that concepts and methodologies developed in the context of isolated gas-phase clusters and atomic nuclei are often most useful for investigations of finitesize solid-state structures. In particular, it has been shown most recently 25,27 through first principles molecular dynamics simulations that as metallic (sodium) nanowires are stretched to just a few atoms in diameter, the reduced dimensions, increased surface-to-volume ratio, and impoverished atomic environment lead to formation of structures made of the metal atoms in the neck, which can be described in terms of those observed in small gas-phase sodium clusters; hence, they were termed supported cluster-deriVed structures (cds). The above prediction of the occurrence of “magic-number” cds in nanowires, due to characteristics of electronic cohesion and atomic bonding in such structures of reduced dimensions, are directly correlated with the energetics of metal clusters, where magic-number sequences of clusters sizes, shapes, and structural motifs due to electronic and/or geometric shell effects have been long predicted and observed. 2,3,28 Furthermore, these results lead one directly to conclude that other properties of nanowires, derived from their energetics, may be described using methodologies developed previously in the context of clusters. Indeed, in this paper, we show that certain aspects of the mechanical response (i.e., elongation force) and electronic transport (e.g., quantized conductance) in metallic nanowires can be analyzed using the local-density-approximation (LDA)-based shell correction method (SCM), developed and applied previously in studies of metal clusters. 3,29 Specifically, we show that in a jellium-modeled, volume-conserving nanowire, variations of the total energy (particularly terms associated with electronic subband corrections) upon elongation of the wire lead to self-selection of a sequence of stable “magic” wire configurations (MWCs, specified in our model by a sequence of the wire’s radii), with the force required to elongate the wire from one configuration to the next exhibiting an oscillatory behavior. Moreover, we show that due to the quantized nature of electronic states in such wires, the electronic conductance varies in a quantized stepwise manner (in units of the conductance quantum g0 ) 2e 2 /h), correlated with the