Quantum Chaos and Metallic Nanocohesion

Convergent semiclassical trace formulae for the density of states and cohesive force of a narrow constriction in an electron gas, whose classical motion is either chaotic or integrable, were derived. It was shown that mode quantization in a metallic point contact or nanowire leads to universal oscillations in its cohesive force: the amplitude of the oscillations depends only on a dimensionless quantum parameter describing the crossover from chaotic to integrable motion, and is of order 1 nano-Newton, in agreement with recent experiments.

Most recently, a linear stability analysis of metallic nanowires was performed in the free-electron model using quantum chaos techniques. It was found that the classical instability of a long wire under surface tension can be completely suppressed by electronic shell effects, leading to stable cylindrical configurations whose electrical conductance is a magic number 1, 3, 5, 6,... times the quantum of conductance. Our results are quantitatively consistent with recent experiments with alkali metal nanowires.

Publications

1. C. A. Stafford, F. Kassubek, J. Bürki, and H. Grabert,
   Universality in metallic nanocohesion: a quantum chaos approach,
   Phys. Rev. Lett. 83 , 4836 (1999).
   
   
2. F. Kassubek, C. A. Stafford, and H. Grabert,
   On universality in metallic nanocohesion,
   Physica B 280 , 438 (2000).
   
   
3. F. Kassubek, C. A. Stafford, H. Grabert, and R. E. Goldstein,
   Quantum Suppression of the Rayleigh Instability in Nanowires,
   Nonlinearity 14 , 167 (2001).
   
   
4. C. A. Stafford, F. Kassubek, and H. Grabert,
   Cohesion and Stability of Metal Nanowires: A Quantum Chaos Approach,
   Adv. Solid State Phys. 41 , 497-511 (2001).
   
   
5. C.-H. Zhang, F. Kassubek, and C. A. Stafford,
   Surface Fluctuations and the Stability of Metal Nanowires,
   Phys. Rev. B 68, 165414 (2003).
   
   
6. J. Bürki, R. E. Goldstein, and C. A. Stafford,
   Quantum Necking in Stressed Metallic Nanowires,
   Phys. Rev. Lett. 91, 254501 (2003).
   
   
7. J. Bürki, C. A. Stafford, and D. L. Stein,
   Fluctuational Instabilities of Alkali and Noble Metal Nanowires,
   in Noise in Complex Systems and Stochastic Dynamics II, edited by Z. Gingl et al. (SPIE Proceedings, 2004), vol. 5471, pp. 367-379.

8. C.-H. Zhang, J. Bürki, and C. A. Stafford,
   Stability of Metal Nanowires at Ultrahigh Current Densities,
   cond-mat/0411058.