1. The Peierls Instability in Metal Nanowires Daniel Urban (Albert-Ludwigs Universität Freiburg, Germany) In collaboration with C.A.Stafford and H.Grabert

2. Peierls Instability is a distortion energetically favorable? max energy gain for EFEF

3. This model requires: good charge screening almost spherical Fermi-surface NFEM is suitable for s-orbital-metals (alkali metals, gold) Nanoscale Free-Electron Model (NFEM) free electrons + confining potential ions = incompressible homogeneous background nanowire = quantum waveguide open system connected to reservoirs scattering problem

4. eigenenergies NFEM: Nanowire = Waveguide transverse wave function (modes, channels) wave function EFEF quantized motion in x-y-plane free motion in z-direction k F,1 k F,n

5. Difference from standard Peierls theory: no periodic boundary conditions Peierls Instability at Length L Cylindrical wire + perturbation Pseudo gap, energy gap only for nanowire with finite length L system = nanowire + leads

6. Surface Phonons Ions = incompressible fluid Born-Oppenheimer approximation Phonon frequency mode stiffness mode inertia Grand canonical potential:

7. Scattering Matrix Formalism density of statesgrand canonical potential

8. Grand canonical potential mode stiffness Mode Stiffness Cylindrical nanowire + perturbation L C : critical length

9. Dispersion Relation

10. CDW Correlations Crossover: L<L C : small fluctuations about cylindrical shape L>L C : CDW with quantum fluctuations, no long-range order

11. Finite-size Scaling Scaling of the mode stiffness: Length scale Energy scale critical length Critical point and

12. Correlation length ξ n ξ is material dependent & tunable by applying strain singular part of the mode stiffness

13. Summary Peierls instability in metal nanowires at L=L C ~ξ Further reading: DFU, Stafford, Grabert, cond-mat/0610787 DFU, Grabert, PRL 91, 256803 Hyperscaling of the singular part of the free energy CDW in metal nanowires should be experimentally observable under strain