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Fishing Bosons in the depths of Fermi Sea. Giorgio Benedek Università di Milano-Bicocca Pavia, 6 March 2014 from a collaboration with: J. Peter Toennies Marco Bernasconi Davide Campi Pedro M. Echenique Evgueni V. Chulkov Irina Sklydneva

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Fishing Bosons

in the depths of Fermi Sea

Giorgio Benedek

Università di Milano-Bicocca

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

  • 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

Angular distributions 1943


  • Inelastic processes:

  • inelastic bound state resonances

  • kinematical focussing

Manson and Celli (1971) 1943

GB (GF formulation, 1973)

displacements of the SURFACE atoms (layer index = 0)

…to a slab of N 1943z layers

Surface phonons 2: from one monolayer…

Longitudinal 1943




Time-of-Flight spectra

U. Harten, J.P. Toennies and Ch. Wöll (1983-85)

The bones and the skin! 1943

  • 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


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)

Why so many phonons? Chulkov, and J. P. Toennies

Milano Göttingen

(Bernasconi, GB) (JPT)

DIPC Karlsruhe

(Chulkov) (Bohnen, Heid)

The quantum sonar effect Chulkov, and J. P. Toennies



Theory: DFPT (mixed plane + spherical wave basis) Chulkov, and J. P. Toennies

for a 5 or 7 ML film on a rigid substrate


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 !

HAS scattering intensities Q = 0

the non-diagonal elements of the electron density matrix act as effective inelastic scattering potential

electron-phonon interaction matrix

electronic susceptibility

mode-selected e-p coupling lambda Q = 0

a slowly varying function

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

Persistent SC in Pb/Si(111) mode-selected electron-phonon coupling constants !

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).

Superconductivity in Pb/Si(111) ultra-thin films mode-selected electron-phonon coupling constants !

Theory predicts also the drop of total l and Tc below 4 ML !

The interface mode is the culprit for SC!


Acoustic Surface Plasmons (ASP) observed by HAS in Cu(111)! mode-selected electron-phonon coupling constants !

ASP mode-selected electron-phonon coupling constants !0


Band structure of graphene mode-selected electron-phonon coupling constants !

Dirac massless fermions

Dirac massive fermions

Graphene / Ru(0001)0 mode-selected electron-phonon coupling constants !

HAS: Daniel Farias (Madrid)

DIRAC mode-selected electron-phonon coupling constants !?

Planck lattice

back to solid

at r = a

Conclusions: mode-selected electron-phonon coupling constants !

 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

new adventures with Otto Stern’s mode-selected electron-phonon coupling constants !

invention, a new life for HAS !

Pavia - Milano

The Cavendish He3 Spin-Echo Apparatus mode-selected electron-phonon coupling constants !

  • Exploiting the old paradox: mode-selected electron-phonon coupling constants !

  • 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...)

The Multipole Expansion (ME) Method mode-selected electron-phonon coupling constants !

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)


Stefano Baroni mode-selected electron-phonon coupling constants !

Density-Functional Perturbation Theory vs. Multipole expansion

ynk Kohn-Sham wave functions:

Adiabatic condition mode-selected electron-phonon coupling constants !

Secular equation

Non-local dielectric response (susceptibility)

Adiabatic dynamic electron density oscillations