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Stability and Symmetry Breaking in Metal Nanowires I: Toward a Theory of Metallic Nanocohesion
Capri Spring School on Transport in Nanostructures, March 29, 2007
Charles Stafford
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.
Surface-tension driven instability
T. R. Powers and R. E. Goldstein, PRL 78, 2555 (1997)
Cannot be overcome in classical MD simulations!
Fabrication of a gold nanowire using an electron microscope
Courtesy of K. Takayanagi, Tokyo Institute of Technology
QuickTime™ and a YUV420 codec decompressor are needed to see this picture.
Courtesy of K. Takayanagi, Tokyo Institute of Technology
Extrusion of a gold nanowire using an STM
Is electron-shell structure the key to understanding stable contact geometries?
A. I. Yanson, I. K. Yanson & J. M. van Ruitenbeek, Nature 400, 144 (1999);PRL 84, 5832 (2000); PRL 87, 216805 (2001)
Corrected Sharvin conductance:
T=90K
Conductance histograms of sodium nanocontacts
2. Nanoscale Free-Electron Model (NFEM)
• 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.
Scattering theory of conduction and cohesion
Electrical conductance (Landauer formula)
Grand canonical potential (independent electrons)
Electronic density of states (Wigner delay)
Adiabatic + WKB approximations
Schrödinger equation decouples:
WKB scattering matrix for each 1D channel:
,
Electron-shell potential
→ 2D shell structure favors certain “magic radii”
Classical periodic orbitsin a slice of the wire
Different constraints possible in NFEM
# of atoms
Physical properties (e.g., tensile force) depend only on energy differences:
3. Conclusions to Lecture 1
Nanoscale Free Electron Model is able to describe quantumtransport and metallic nanocohesion on an equal footing,explaining observed correlations in force and conductance ofmetal nanocontacts.
Total energy calculations apparently not sufficient to addressnanowire stability.
What more is needed? See Lecture 2!