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Fishing Bosons in the depths of Fermi Sea
Giorgio BenedekUniversità di Milano-Bicoccahttp://www2.mater.unimib.it/utenti/benedek/
Pavia, 6 March 2014
from a collaboration with:J. Peter ToenniesMarco BernasconiDavide CampiPedro M. EcheniqueEvgueni V. ChulkovIrina SklydnevaKlaus-Peter BohnenRolf HeidVasse Chis
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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
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Welcome to the Fermi Sea
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Otto Stern (Sohrau 1888 – Berkeley 1969) Nobel Laureate 1943
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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
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Supersonic nozzle beam sources
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J. P. Toennies: HUGO (MPI-SF, Goettingen)
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Angular distributions
Diffraction
Inelastic processes: - inelastic bound state resonances - kinematical focussing
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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)
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Surface phonons 2: from one monolayer…
…to a slab of Nz layers
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Rayleighwave
Longitudinalresonance
U. Harten, J.P. Toennies and Ch. Wöll (1983-85)
Time-of-Flight spectra
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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
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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)
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Phonon-induced surface charge-density oscillations
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Milano Göttingen (Bernasconi, GB) (JPT)
DIPC Karlsruhe (Chulkov) (Bohnen, Heid)
Why so many phonons?
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The quantum sonar effect
Bi(111)
Pb(111)
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Theory: DFPT (mixed plane + spherical wave basis)
for a 5 or 7 ML film on a rigid substratePb/Cu(111)
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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 !
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),()( 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
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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
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HAS from metal surfaces and thin films can measure the mode-selected electron-phonon coupling constants !
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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 !
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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!
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Acoustic Surface Plasmons (ASP) observed by HAS in Cu(111)!
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ASP
ASP0
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Band structure of graphene
Dirac massless fermions
Dirac massive fermions
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Graphene / Ru(0001)0
HAS: Daniel Farias (Madrid)
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DIRAC?
|2/1|
1
KK UTm
m
m
KTK 2
)( 2
mm
4222)( cmcppE
mKcqKp 2/),(
32,
c
hGa
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hcmm PP Planck lattice
P
mmGmmc
)(21910
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m
m
mm
eV1.04
)(2
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r
mm
am
hrV eh
eh at r = aback to solid
r
hc
m
mrV
PG
Δ)(
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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:
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new adventures with Otto Stern’sinvention, a new life for HAS !
Pavia - Milano R.do
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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
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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...)
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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)
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.'',2
1
],',[2
1
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,
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jll
ll
llo
lclcllH
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ll YYnnErdrdV
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llRllR
rrnrd
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lulu
EllR
elion
llll
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v
![Page 37: Fishing Bosons in the depths of Fermi Sea Giorgio Benedek Università di Milano-Bicocca Pavia, 6 March 2014.](https://reader035.fdocuments.us/reader035/viewer/2022062519/5697bfe11a28abf838cb4049/html5/thumbnails/37.jpg)
Density-Functional Perturbation Theory vs. Multipole expansion
..)'(
)r(
)(2
)'()(
)r(2)',(
kk
k
kk
2
k cclulululu
llRocc
vv
ionvocc
vv
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el
vv
k Kohn-Sham wave functions: )(rkkk
nvv
occ
v
elionocc
vv
ionv R
lulunrd
lulu 0
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kk
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k )'()(
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)(
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)r(
)(
vv
vv
Stefano Baroni
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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