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Stability and Symmetry Breaking in Metal Nanowires II: Linear Stability Analyses

Explore the linear stability and symmetry breaking in metal nanowires through comprehensive analyses, considering various cross-section shapes and material influences.

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Stability and Symmetry Breaking in Metal Nanowires II: Linear Stability Analyses

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  1. Charles Stafford Stability and Symmetry Breaking in Metal Nanowires II: Linear Stability Analyses D. F. Urban, J. Bürki, C.-H. Zhang, C. A. Stafford & H. Grabert, PRL 93, 186403 (2004) Capri Spring School on Transport in Nanostructures, March 29, 2007

  2. Electron-shell potential

  3. 1. Linear stability analysis of a cylinder Mode stiffness: Classical (Rayleigh) stability criterion:

  4. 1. Linear stability analysis of a cylinder (m=0) Mode stiffness: Classical (Rayleigh) stability criterion:

  5. Mode stiffness α(q) F. Kassubek, CAS, H. Grabert & R. E. Goldstein, Nonlinearity 14, 167 (2001)

  6. Stability under axisymmetric perturbations A>0 C.-H. Zhang, F. Kassubek & CAS, PRB 68, 165414 (2003)

  7. Stability of nanocylinders at ultrahigh current densities Generalized free energy for ballistic nonequilibrium electron distribution. Coulomb interactions included in self-consistent Hartree approximation. ! C.-H. Zhang, J. Bürki & CAS, PRB 71, 235404 (2005)

  8. 2. General linear stability analysis General cross section: Free energy: Stability requires: • Stationarity • Convexity

  9. General stability analysis of a cylinder D. Urban, J. Bürki, CAS & H. Grabert PRB 74, 245414 (2006)

  10. 3. Stable elliptical nanowires D. F. Urban, J. Bürki, C.-H. Zhang, CAS & H. Grabert, PRL 93, 186403 (2004)

  11. Combining cylindrical and elliptical structures: Theory of shell and supershell effects in nanowires D. F. Urban, J. Bürki, C.-H. Zhang, CAS & H. Grabert, PRL 93, 186403 (2004)

  12. Combining cylindrical and elliptical structures: Theory of shell and supershell effects in nanowires • Magic cylinders ~75% of most-stable wires. • Supershell structure: most-stable elliptical wires occur at the nodes • of the shell effect. D. F. Urban, J. Bürki, C.-H. Zhang, CAS & H. Grabert, PRL 93, 186403 (2004)

  13. Comparison of experimental shell structure for Na with predicted most stable Na nanowires Exp: A. I. Yanson, I. K. Yanson & J. M. van Ruitenbeek, Nature 400, 144 (1999) Theory: D. F. Urban, J. Bürki, C.-H. Zhang, CAS & H. Grabert, PRL 93, 186403 (2004) Discussion: D. F. Urban et al., Solid State Comm. 131, 609 (2004)

  14. 4. Quadrupolar cross sections D. Urban, J. Bürki, CAS & H. Grabert PRB 74, 245414 (2006)

  15. Elliptical vs. quadrupolar cross sections Quadrupole favored for large deformations due to reduced surface energy. For ε < 1.3, quadrupole ≈ ellipse. No generically preferred shape; can be positive or negative. → Integrable cross sections not special (except cylinder)

  16. Higher multipole deformations Higher-m deformations less stable due to increased surface energy. D. Urban, J. Bürki, CAS & H. Grabert PRB 74, 245414 (2006)

  17. 5. Material dependence of stability Na Relative stability of deformed structures depends on surface tension in natural units: Absolute stability also depends on ; → Lecture 3. Au

  18. Special case: Aluminum Two different types of histograms (history dependent) Crossover from electronic to atomic shell effects at A. I. Mares, D. F. Urban, J. Bürki, H. Grabert, CAS & J. M. van Ruitenbeek, cond-mat/0703589

  19. Extracting individual conductance peaks A. I. Mares, D. F. Urban, J. Bürki, H. Grabert, CAS & J. M. van Ruitenbeek, cond-mat/0703589

  20. Linear stability analysis for Aluminum Trivalent metal; Fermi surface free-electron like in extended-zone scheme. Physics of Al clusters suggests NFEM applicable for → Same magic sequence, but relative stability of deformed wires enhanced. A. I. Mares, D. F. Urban, J. Bürki, H. Grabert, CAS & J. M. van Ruitenbeek, cond-mat/0703589

  21. Electron-shell structure: Theory vs. Experiment A. I. Mares, D. F. Urban, J. Bürki, H. Grabert, CAS & J. M. van Ruitenbeek, cond-mat/0703589

  22. Superdeformed nanowires cf. Physics of superdeformed nuclei A. I. Mares, D. F. Urban, J. Bürki, H. Grabert, CAS & J. M. van Ruitenbeek, cond-mat/0703589

  23. 6. Conclusions • Cylinders are special: • Only generically stable shape. • Analogy to shell-effects in clusters and nuclei; • quantum-size effects in thin films. • Open questions: • Structural dynamics (Urban seminar, Lecture 3) • Putting the atoms back in…

  24. Putting the atoms back in Left (experiment): Y. Kondo & K. Takayanagi, Science289, 606 (2000) Right (theory): Dennis Conner, Nate Riordan, J. Bürki & CAS (unpublished)

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