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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 2014at 16 PM, Aula 102
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)
Welcome to the Fermi Sea
Otto Stern (Sohrau 1888 – Berkeley 1969) Nobel Laureate 1943
Otto Stern, O.R. Frisch, I. Estermann (Hamburg, 1929-1933).
He
NaCl(001)
[meV]
542.4
][Å
2[Å]
1iEk
),(2
),(
nma
kkk ifz
GG K
Kk
a
Supersonic nozzle beam sources
J. P. Toennies: HUGO (MPI-SF, Goettingen)
Angular distributions
Diffraction
Inelastic processes: - inelastic bound state resonances - kinematical focussing
iffiiz
f
ff
)(
EGEnk
dΩdE
d
kFF
)Δ(Im|)(1|
12
v i-EE
EGvif
QQ uu
0
)0()0()Δ(
*
Manson and Celli (1971)
GB (GF formulation, 1973)
displacements of the SURFACE atoms (layer index = 0)
Surface phonons 2: from one monolayer…
…to a slab of Nz layers
Rayleighwave
Longitudinalresonance
U. Harten, J.P. Toennies and Ch. Wöll (1983-85)
Time-of-Flight spectra
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
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)
Phonon-induced surface charge-density oscillations
Milano Göttingen (Bernasconi, GB) (JPT)
DIPC Karlsruhe (Chulkov) (Bohnen, Heid)
Why so many phonons?
The quantum sonar effect
Bi(111)
Pb(111)
Theory: DFPT (mixed plane + spherical wave basis)
for a 5 or 7 ML film on a rigid substratePb/Cu(111)
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 !
),()( tnA,tV rr
'''
( ) ( )( ) ( , ; )n n'
n, nnnn n
f if n i A g
E E
K K+Q
K QK K Q Q
r rr K K + Q
vkvn fiBE
i
f
ff
)(
EnVEnk
dΩdE
dQ QK QK )(),()](1[
212
HAS scattering intensities
the non-diagonal elements of the electron density matrix act as effective inelastic
scattering potential
electron-phonon interaction matrix
02 2
0
( , )( , )
1 (4 / ) ( , )e Q
Qelectronic susceptibility
v vvFff
EENEfdΩdE
dQ QQ )()()(
)1(2
)()(2
1)()();,( 32
' ' QQQK QKK rrQKK IENifg Fn n n'nnn
mode-selected e-p coupling lambda
a slowly varying function
HAS from metal surfaces and thin films can measure the mode-selected electron-phonon coupling constants !
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 !
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!
Acoustic Surface Plasmons (ASP) observed by HAS in Cu(111)!
ASP
ASP0
Band structure of graphene
Dirac massless fermions
Dirac massive fermions
Graphene / Ru(0001)0
HAS: Daniel Farias (Madrid)
DIRAC? gravity as a quantum effect in a granular space
|2/1|
1
KK UTm
m
m
KTK 2
)( 2
mm
4222)( cmcppE
mKcqKp 2/),(
32,
c
hGa
G
hcmm PP Planck lattice
P
mmGmmc
)(21910
Pm
m
m
mm
eV1.04
)(2
2
r
mm
am
hrV eh
eh at r = aback to solid
r
hc
m
mrV
PG
Δ)(
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,...
3He spin-echo spectroscopy
New trends: Bi(111), and TIs: Sb(111), Bi2Se3 ,... TU Graz
HAS can measure acoustic surface plasmons
New extraordinary possibilities:
new adventures with Otto Stern’sinvention, a new life for HAS !
Pavia - Milano R.do
Parameter Value
Total scattering angle 44.4 degrees
3He Angular Resolution 0.1 degree
Nominal beam energy 8 meV
Measured beam intensity 1e14 atoms/second
Beam diameter at target 2 mm
Energy resolution (QE peak width) 20 neV
Scattering chamber base pressure 2e-10 mbar
Sample manipulator 6 axis, titanium
Sample manipulator resolution 0.003 degrees
Sample heating Radiation / E-beam
Sample cooling Liquid Nitrogen or Helium
Sample temperature range 55 K - >1200 K
The Cavendish He3 Spin-Echo Apparatus
APPENDIX I:
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...)
APPENDIX II: Further conclusions
APPENDIX III: The Multipole Expansion (ME) Method
rdnnFEE ionion 3)()()]([ rrr v
))(()( ll llion urrr vv
)()()( ,0 lclClC
,Γ,0 llcE
Equilibrium:
ll YlCn rrr
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)
.'',2
1
],',[2
1
,2
1
, '
,
,
jll
ll
llo
lclcllH
lclullTllT
lulullREE
,
1
,
3
3
2
lI
l
Ylurd
YlunErdV
lcluEllT
rrrv
rrr
,1
'',
'233
2
'2
'
ll YYnnErdrdV
lclcEllH
rrrrrr
.)',()',(
)r-r()r(
)'()()'()()',(
,0
23
'
22
llRllR
rrnrd
lulu
E
lulu
EllR
elion
llll
ion
v
Density-Functional Perturbation Theory vs. Multipole expansion
..)'(
)r(
)(2
)'()(
)r(2)',(
kk
k
kk
2
k cclulululu
llRocc
vv
ionvocc
vv
ionv
el
vv
k Kohn-Sham wave functions: )(rkkk
nvv
occ
v
elionocc
vv
ionv R
lulunrd
lulu 0
23
kk
2
k )'()(
)r()r(
)'()(
)r(
vv
TTHlulu
dd
lulu
nrdcc
lulu
ionion
ionocc
vv
ionv
133
3
kk
k
)'(
)'r()'r,r(
)(
)r('rr
)'(
)r(
)(
)r(..
)'(
)r(
)(
vv
vv
Stefano Baroni
Adiabatic condition uc TH 1
νTTHRRνM elion QuQu )( 10
2Q
Secular equation
Adiabatic dynamic electron density oscillations
l lion tlrd,tn ),(/)(),()( 3 urrrrr v
Non-local dielectric response (susceptibility)
).(),()( )',( '''331
' ll YYrdrdllH rrrrrr
