1. Fishing Bosons in the depths of Fermi Sea Giorgio Benedek Università di Milano-Bicocca http://www2.mater.unimib.it/utenti/benedek/ Pavia, 6 March 2014 from a collaboration with: J. Peter Toennies Marco Bernasconi Davide Campi Pedro M. Echenique Evgueni V. Chulkov Irina Sklydneva Klaus-Peter Bohnen Rolf Heid Vasse Chis

2. Condensed matter: the Fermion & Boson zoo Fermions: - electrons, holes, protons, neutrons, - neutral atoms (A = odd) Bosons: - photons - Cooper pairs - neutral atoms (A =even) - Elementary excitations (and their quanta) - e-h pairs, excitons - phonons - plasmons - magnons - rotons - polaritons - plasmarons

3. Welcome to the Fermi Sea

4. Otto Stern (Sohrau 1888 – Berkeley 1969) Nobel Laureate 1943

5. Otto Stern, O.R. Frisch, I. Estermann (Hamburg, 1929-1933). He NaCl(001) a

6. Supersonic nozzle beam sources

7. J. P. Toennies: HUGO (MPI-SF, Goettingen)

8. Angular distributions Diffraction Inelastic processes: - inelastic bound state resonances - kinematical focussing

9. Manson and Celli (1971) GB (GF formulation, 1973) displacements of the SURFACE atoms (layer index = 0)

10. Surface phonons 2: from one monolayer… …to a slab of N z layers

11. Rayleigh wave Longitudinal resonance U. Harten, J.P. Toennies and Ch. Wöll (1983-85) Time-of-Flight spectra

12. Questions: 1) Why the longitudinal resonance is so soft? 2)Why is it observed at all? 3)Why is it found in ALL metals? The bones and the skin! Bibi Giorgio, Vittorio & Peter

13. V. Chis, B. Hellsing, G. Benedek, M. Bernasconi, E. V. Chulkov, and J. P. Toennies “Large Surface Charge-density Oscillations Induced by Subsurface Phonon Resonances” Phys. Rev. Letters, 101, 206102 (2008) DFPT + SCDO for Cu(111)

14. Phonon-induced surface charge-density oscillations

15. Milano Göttingen (Bernasconi, GB) (JPT) DIPC Karlsruhe (Chulkov) (Bohnen, Heid) Why so many phonons?

16. The quantum sonar effect Bi(111) Pb(111)

18. Theory: DFPT (mixed plane + spherical wave basis) for a 5 or 7 ML film on a rigid substrate Pb/Cu(111)

20. Surface charge density oscillations of the topmost modes at Q = 0 5 ML Pb/rigid substrate Almost identical SCDO’s for two completely different modes: just as found in HAS experiments! HAS perceives underground phonons (5 layers deep) via e-p interaction !

21. HAS scattering intensities the non-diagonal elements of the electron density matrix act as effective inelastic scattering potential electron-phonon interaction matrix electronic susceptibility

22. mode-selected e-p coupling lambda a slowly varying function

23. HAS from metal surfaces and thin films can measure the mode-selected electron-phonon coupling constants !

24. T. Zhang, P. Cheng, W.-J. Li, Y.-J. Sun, G. Wang, X.-G. Zhu, K. He, L. Wang, X. Ma, X. Chen, Y. Wang, Y. Liu, H.-Q. Lin, J.F. J ia, and Q.-K. Xue, Nature Physics 6, 104-108 (2010). S. Qin, J. Kim, Q. Niu, and C.-K. Shih, Science 324,1314 (2009). Persistent SC in Pb/Si(111) 16 ML down to 1 !

25. Theory predicts also the drop of total and Tc below 4 ML ! Superconductivity in Pb/Si(111) ultra-thin films 1 The interface mode is the culprit for SC!

26. Acoustic Surface Plasmons (ASP) observed by HAS in Cu(111)!

27. ASP ASP 0

28. Band structure of graphene Dirac massless fermions Dirac massive fermions

29. Graphene / Ru(0001)0 HAS: Daniel Farias (Madrid)

30. DIRAC ? Planck lattice at r = a back to solid

31. Conclusions:  HAS can measure deep sub-surface phonons in metal films: a complete spectroscopy (not accessible to other probes such as EELS)  HAS can directly measure the mode-selected electron-phonon coupling in metals: a fundamental information a) for the theory of 2D superconductivity b) for the theory of IETS (STS) intensities c) for understanding phonon-assisted surface reactions, etc. d) chiral symmetry break: graphene, topological insulators,...  3 He spin-echo spectroscopy  New trends: Bi(111), and TIs: Sb(111), Bi 2 Se 3,...  TU Graz  HAS can measure acoustic surface plasmons  New extraordinary possibilities:

32. new adventures with Otto Stern’s invention, a new life for HAS ! Pavia - Milano R.do

33. ParameterValue Total scattering angle44.4 degrees 3He Angular Resolution0.1 degree Nominal beam energy8 meV Measured beam intensity1e14 atoms/second Beam diameter at target2 mm Energy resolution (QE peak width)20 neV Scattering chamber base pressure2e-10 mbar Sample manipulator6 axis, titanium Sample manipulator resolution0.003 degrees Sample heatingRadiation / E-beam Sample coolingLiquid Nitrogen or Helium Sample temperature range55 K - >1200 K The Cavendish He3 Spin- Echo Apparatus

34. Exploiting the old paradox: - impact EELS doesn’t see valence electrons! - neutral atoms interact inelastically via valence electrons!! - phonons via electron-phonon interaction - acoustic surface plasmons - surface excitons in insulators (with keV neutrals: H. Winter et al) - with 3He spin echo: slow dynamics (diffusion) magnetic excitations (?) - plasmarons (topological insulators, graphene...)

35. The Multipole Expansion (ME) Method Equilibrium: C.S. Jayanthi, H. Bilz, W. Kress and G. Benedek, Phys. Rev. Letters 59, 795 (1987) (after an idea of Phil Allen for the superconducting phonon anomalies of Nb)

37. Density-Functional Perturbation Theory vs. Multipole expansion  k Kohn-Sham wave functions: Stefano Baroni

38. Adiabatic condition Secular equation Adiabatic dynamic electron density oscillations Non-local dielectric response (susceptibility)