Abstract
Notwithstanding the discreteness of metallic constrictions, it is shown that the finite elasticity of stable, single-atom gold constrictions allows for a continuous and reversible change in conductance, thereby enabling observation of channel saturation and conductance quantization. The observed channel saturation and signature for conductance quantization is achieved by superposition of atomic/subatomic-scale oscillations on a retracting/approaching gold tip against a gold substrate of a scanning probe. Results also show that conductance histograms are neither suitable for evaluating the stability of atomic configurations through peak positions or peak height nor appropriate for assessing conductance quantization. A large number of atomic configurations with similar conductance values give rise to peaks in the conductance histogram. The positions of the peaks and counts at each peak can be varied by changing the conditions under which the histograms are made. Histogram counts below 1Go cannot necessarily be assumed to arise from single-atom constrictions.
Highlights
A characteristic sequence of peaks was reported in sodium conductance histogramspeaks at 1Go, 3Go, 5Go, and 6Go, with peaks at 2, 4, and 7Go being absentas a signature of conductance quantization44 ͑even though a small but well-defined peak is observed at 2Go in both Na and K histograms45͒
Two of the authors in Ref. 44 questioned the use of histogram peaks as proof of conductance quantization, instead reinterpreting them as arising from preferred atomic configurations.[46]. These authors noted that their original interpretation of the characteristic sequence of peaks in Na histogram[44] as a signature of conductance quantization would be “difficult to explain by other models,” while adding that the role of preferred atomic arrangements has to be considered in interpreting the histograms.[46]
The above discussion shows that the current interpretation of conductance histograms recognizes the limitations of histogram peaks, the origin of the histogram peaks remains unclear and their use remains prevalent in the literature
Summary
Realization of atomic-sized metal or metal-molecule electronics devices[1,2,3,4] requires a fundamental understanding of conditions under which conductance quantization prevails,[5] their electronic structure and regulation of electron transmission behavior,[6,7,8,9,10,11,12,13,14,15,16,17,18,19] and their mechanical stability against disruptive forces of entropic thermal fluctuations.[20,21,22,23] In addition, positioning and manipulation of individual atoms requires a basic understanding of operative forces[24,25,26,27] and an ability to measure them.[28,29,30,31,32,33,34,35,36,37] Quantization of conductance was first shown experimentally in a two-dimensional electron gas.[38,39] Similar studies on atomic-sized metal point contacts pose experimental challenges owing to the difficulty in continuously varying the diameter of the constriction on the scale of the Fermi wavelengthon the same order of interatomic distanceswithout causing an atomic rearrangement. Simultaneous measurements of conductance and force in gold constrictions show that a stepwise change in conductance is accompanied by a stepwise change in force, indicating a concomitant atomic rearrangement within the constriction.[36,37,40,41] To extract the signature of conductance quantization, conductance histograms were initially introduced.[42,43] From such histograms, it was posited that even though the observed conductance may assume integer and noninteger values of Go=2e2 / h, the quantum of conductance; e is quantum of charge and h is Planck constant, the fact that peaks only occur at or near integers of Go constitutes or at least strongly suggests conductance quantization.[42,43] In addition, a characteristic sequence of peaks was reported in sodium conductance histogramspeaks at 1Go, 3Go, 5Go, and 6Go, with peaks at 2, 4, and 7Go being absentas a signature of conductance quantization44 ͑even though a small but well-defined peak is observed at 2Go in both Na and K histograms45͒. Combined with noise analysis of conductance plateaus, the origin of peaks in conductance histograms is explained
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