stability and symmetry breaking in metal nanowires i: toward a theory of metallic nanocohesion
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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.
1. How thin can a metal wire be?
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
What is holding the wires together? A mechanical analogue of conductance quantization?
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)
Quantum suppression of Shot noise
NFEM w/disorder
Gold nanocontacts
Multivalent atoms
Adiabatic + WKB approximations
Schrödinger equation decouples:
WKB scattering matrix for each 1D channel:
,
Comparison: NFEM vs. experiment
Exp:Theory:
Weyl expansion + Strutinsky theorem
Mean-field theory:
Weyl expansion:
Electron-shell potential
→ 2D shell structure favors certain “magic radii”
Classical periodic orbitsin a slice of the wire
NFEM vs. self-consistent Jellium calculation
Different constraints possible in NFEM
# of atoms
Physical properties (e.g., tensile force) depend only on energy differences:
Example of the Strutinsky theorem: self-consistentHartree approximation
Special case: the constant-interaction model
Last term is important!
Semiclassical power counting
Planck’s constant:
→ Surface energy dominates shell correction?!
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!
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