Cohesion and Stability of Metal Nanowires: A Quantum Chaos Approach
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A remarkably quantitative understanding of the electrical and mechanical properties of metal wires with a thickness on the scale of a nanometer has been obtained within the free-electron model using semiclassical techniques. Convergent trace formulas for the density of states and cohesive force of a narrow constriction in an electron gas, whose classical motion is either chaotic or integrable, are derived. Mode quantization in a metallic point contact or nanowire leads to universal oscillations in its cohesive force, whose amplitude depends only on a dimensionless quantum parameter describing the crossover from chaotic to integrable motion, and is of order 1nN, in agreement with experiments on gold nanowires. A linear stability analysis shows that the classical instability of a long wire under surface tension can be completely suppressed by quantum effects, leading to stable cylindrical configurations whose electrical conductance is a magic number 1, 3, 5, 6,... times the conductance quantum, in accord with recent results on alkali metal nanowires.
14 pages, 11 figures, lecture given at the Symposium on 30 Years of the Gutzwiller Trace Formula, German Physical Society Meeting, Hamburg, March 28, 2001
14 pages, 11 figures, lecture given at the Symposium on 30 Years of the Gutzwiller Trace Formula, German Physical Society Meeting, Hamburg, March 28, 2001