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Stability and Symmetry Breaking in Metal Nanowires I: Toward a Theory of Metallic Nanocohesion

Charles Stafford. Stability and Symmetry Breaking in Metal Nanowires I: Toward a Theory of Metallic Nanocohesion. Capri Spring School on Transport in Nanostructures, March 29, 2007. Acknowledgements. Students: Chang-hua Zhang (Ph.D. 2004) Dennis Conner (M.S. 2006) Nate Riordan Postdoc:

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Stability and Symmetry Breaking in Metal Nanowires I: Toward a Theory of Metallic Nanocohesion

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  1. Charles Stafford Stability and Symmetry Breaking in Metal Nanowires I: Toward a Theory of Metallic Nanocohesion Capri Spring School on Transport in Nanostructures, March 29, 2007

  2. Acknowledgements Students: Chang-hua Zhang (Ph.D. 2004) Dennis Conner (M.S. 2006) Nate Riordan Postdoc: Jérôme Bürki Coauthors: Dionys Baeriswyl, Ray Goldstein, Hermann Grabert, Frank Kassubek, Dan Stein, Daniel Urban Funding: NSF Grant Nos. DMR0072703 and DMR0312028; Research Corp.

  3. 1. How thin can a metal wire be?

  4. Surface-tension driven instability Cannot be overcome in classical MD simulations! T. R. Powers and R. E. Goldstein, PRL 78, 2555 (1997)

  5. Fabrication of a gold nanowire using an electron microscope Courtesy of K. Takayanagi, Tokyo Institute of Technology

  6. Extrusion of a gold nanowire using an STM Courtesy of K. Takayanagi, Tokyo Institute of Technology

  7. What is holding the wires together? A mechanical analogue of conductance quantization?

  8. Is electron-shell structure the key to understanding stable contact geometries? Conductance histograms of sodium nanocontacts Corrected Sharvin conductance: T=90K A. I. Yanson, I. K. Yanson & J. M. van Ruitenbeek, Nature 400, 144 (1999); PRL 84, 5832 (2000); PRL 87, 216805 (2001)

  9. Model nanowire as a free-electron gas confined by hard walls. Ionic background = incompressible fluid. Most appropriate for s-electrons in monovalent metals. Regime: Metal nanowire = 3D open quantum billiard. 2. Nanoscale Free-Electron Model (NFEM)

  10. Scattering theory of conduction and cohesion Electrical conductance (Landauer formula) Grand canonical potential (independent electrons) Electronic density of states (Wigner delay)

  11. Quantum suppression of Shot noise NFEM w/disorder Gold nanocontacts

  12. Multivalent atoms

  13. Adiabatic + WKB approximations Schrödinger equation decouples: WKB scattering matrix for each 1D channel: ,

  14. Comparison: NFEM vs. experiment Exp: Theory:

  15. Weyl expansion + Strutinsky theorem Mean-field theory: Weyl expansion:

  16. Electron-shell potential Classical periodic orbits in a slice of the wire → 2D shell structure favors certain “magic radii”

  17. NFEM vs. self-consistent Jellium calculation

  18. Different constraints possible in NFEM # of atoms Physical properties (e.g., tensile force) depend only on energy differences:

  19. Example of the Strutinsky theorem: self-consistent Hartree approximation

  20. Special case: the constant-interaction model Last term is important!

  21. Semiclassical power counting Planck’s constant: → Surface energy dominates shell correction?!

  22. 3. Conclusions to Lecture 1 Nanoscale Free Electron Model is able to describe quantum transport and metallic nanocohesion on an equal footing, explaining observed correlations in force and conductance of metal nanocontacts. Total energy calculations apparently not sufficient to address nanowire stability. What more is needed? See Lecture 2!

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