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The Quantum Sonar: fishing (for) bosons in the depths of Fermi Sea

This lecture discusses the fermions and bosons found in condensed matter physics, exploring elementary excitations and their quanta. It also presents the concept of surface charge-density oscillations induced by subsurface phonon resonances.

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The Quantum Sonar: fishing (for) bosons in the depths of Fermi Sea

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  1. The Quantum Sonar: fishing (for) bosons in the depths of Fermi Sea Giorgio Benedek Dipartimento di Scienza dei Materiali,Università di Milano-Bicocca (UNIMIB) & Donostia International Physics Center (DIPC) San Sebastian, Spain University of Pavia Volta Lecture Thursday 6 March 2014 at 16 PM, Aula 102

  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 from a collaboration with: J. Peter Toennies (MPI-DS), Marco Bernasconi. Davide Campi (UNIMIB) Pedro M. Echenique, Evgueni V. Chulkov, Irina Sklydneva (DIPC) Klaus-Peter Bohnen, Rolf Heid (KFA) Vasse Chis (Univ. Goteborg)

  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 a NaCl(001)

  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. …to a slab of Nz layers Surface phonons 2: from one monolayer…

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

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

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

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

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

  18. 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 !

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

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

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

  22. Persistent SC in Pb/Si(111) 16 ML down to 1 ! 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 Physics6, 104-108 (2010). S. Qin, J. Kim, Q. Niu, and C.-K. Shih, Science 324,1314 (2009).

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

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

  25. ASP0 ASP

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

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

  28. DIRAC? gravity as a quantum effect in a granular space Planck lattice back to solid at r = a

  29. 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 • for the theory of 2D superconductivity • for the theory of IETS (STS) intensities • for understanding phonon-assisted surface reactions, etc. • chiral symmetry break: graphene, topological insulators,...  HAS can measure acoustic surface plasmons New trends: Bi(111), and TIs: Sb(111), Bi2Se3 ,...  TU Graz  New extraordinary possibilities:  3He spin-echo spectroscopy

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

  31. APPENDIX I: The Cavendish He3 Spin-Echo Apparatus

  32. APPENDIX II: Further conclusions • 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...)

  33. APPENDIX III: The Multipole Expansion (ME) Method 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) Equilibrium:

  34. Stefano Baroni Density-Functional Perturbation Theory vs. Multipole expansion ynk Kohn-Sham wave functions:

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

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