Transcript Diapositiva 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
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) 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
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
[Å] 2
k
[Å 1 ] 4 .
542
E i
[meV]
k
(
K
,
k z
)
K
k f
G G
k i
2
a
(
m
,
n
)
a
NaCl(001)
Supersonic nozzle beam sources
J. P. Toennies: HUGO (MPI-SF, Goettingen)
Diffraction Inelastic processes: - inelastic bound state resonances - kinematical focussing Angular distributions
d
2
(
1
) dE f dΩ f
k f k iz
| 1
n
(
E
) |
F
fi
Im
G
( Δ
E
)
F
if
Manson and Celli (1971) GB (GF formulation, 1973)
G
( Δ
E
)
Q
v
u
*
Q
E f -E i
( 0 )
u Q
Q
v
( 0 )
i
0
displacements of the SURFACE atoms (layer index = 0)
…to a slab of N z layers Surface phonons 2: from one monolayer…
Time-of-Flight spectra Longitudinal resonance Rayleigh wave U. Harten, J.P. Toennies and Ch. Wöll (1983-85)
The bones and the skin!
Questions: 1) Why the longitudinal resonance is so soft? 2) Why is it observed at all?
3) Why is it found in ALL metals?
Giorgio, Vittorio & Peter Bibi
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
Why so many phonons?
Milano G öttingen (Bernasconi, GB) (JPT) DIPC Karlsruhe (Chulkov) (Bohnen, Heid)
Bi(111) Pb(111)
The quantum sonar effect
Theory: DFPT (mixed plane + spherical wave basis) for a 5 or 7 ML film on a rigid substrate
Pb/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 !
HAS scattering intensities
d
2
(
1
) dE f dΩ f
k f k i
[ 1
n BE
(
E
)]
K
n
V fi
(
K
n
,
Q
) 2 (
E
Q
v
)
V
(
r
,t
)
A
n
(
r
,
t
) the non-diagonal elements of the electron density matrix act as effective inelastic scattering potential
f
n
i
A
n
'
f
K
n E
K
n
E
K +Q
n' n
'
Q
i g nn
' 0
e
2 /
Q
2 ) 0 electron-phonon interaction matrix electronic susceptibility
mode-selected e-p coupling lambda
n
K
n
'
g nn
' (
K
,
K
Q
; )
f
K
n
(
r
)
K
Q
n'
(
r
)
i
2 1 2
N
(
E F
) 3
Q
Q
I
(
Q
)
d
2 ( 1 )
dE f dΩ f
f
(
E
)
N
(
E F
)
Q
v
Q
v
(
E
Q
v
) 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) 16 ML down to 1 !
S. Qin, J. Kim, Q. Niu, and C.-K. Shih, Science
324
,1314 (2009).
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).
1 Superconductivity in Pb/Si(111) ultra-thin films Theory predicts also the drop of total and Tc below 4 ML ! The interface mode is the culprit for SC!
Acoustic Surface Plasmons (ASP) observed by HAS in Cu(111)!
ASP ASP 0
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
p
(
K
q
),
c
K
/ 2
m E
(
p
)
p
2
c
2
m
2
c
4
m
m
| 1
T K
1 / 2
U K
|
T K
(
K
) 2 2
m m
m
m
m
m
m
m P
10 19 Planck lattice
c
2 (
m
m
)
m
m P
hc
,
G
2
a
P
hG c
3
G m
m
P V G
(
r
) Δ
m hc m P r
back to solid
V eh
(
r
)
h
2 4
am
2
m h
m e r
0 .
1 eV at
r = a
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,...
HAS can measure acoustic surface plasmons New trends: Bi(111), and TIs: Sb(111), Bi 2 Se 3 ,... New extraordinary possibilities:
TU Graz
3 He spin-echo spectroscopy
new adventures with Otto Stern’s invention, a new life for HAS !
Pavia Milano R.do
APPENDIX I: The Cavendish He3 Spin Echo Apparatus
Parameter
Total scattering angle 3He Angular Resolution Nominal beam energy Measured beam intensity Beam diameter at target Energy resolution (QE peak width) Scattering chamber base pressure Sample manipulator Sample manipulator resolution Sample heating Sample cooling Sample temperature range
Value
44.4 degrees 0.1 degree 8 meV 1e14 atoms/second 2 mm 20 neV 2e-10 mbar 6 axis, titanium 0.003 degrees Radiation / E-beam Liquid Nitrogen or Helium 55 K - >1200 K
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...)
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)
E
E ion
F
[
n
(
r
)]
v ion
(
r
)
n
(
r
)
d
3
r v ion
(
r
)
l v l
(
r
r
l
u
(
l
))
n l
C
r
r
l
C
(
l
)
C
0 , (
l
)
c
(
l
) Equilibrium:
E
c
0 Γ,
l
,
E
E o
1 2
l
,
l
R
l l u
l u
l
1 2
l
,
l
[
T
l
,
l
T
l
' ,
l
]
u
1 2
l
,
l
j H
'
l
,
l
'
c
.
R
(
l
,
l
' ) 2
E
u
(
l
)
u
(
l
' )
u
(
l
2
E ion
)
u
(
l
' )
ll
'
d
3
r n
( r ) 2
v
l
r
( r -
r
r
l
)
R ion
(
l
,
l
' )
R el
0 , (
l
,
l
' ) .
T
l
,
l
2
E
u
l
c
V
1
d
3
r d
3
r
v
I
E
n
u
u
l l
Y
r
r
l
Y
r
r
l
,
H
'
l
,
l
'
V
1 2 2
E
c
d
3
r d
3
r
c
' 2
E l
n
r
n
r
Y
r
r
l
r
r
l
' ,
Stefano Baroni Density-Functional Perturbation Theory vs. Multipole expansion
R el
(
l
,
l
' ) 2
occ
v
k
v
k
u
2 (
l
v
)
ion
(
u
r ) (
l
' )
v
k 2
occ
v
k
u
v
k (
l
)
v
ion
u
(
l
( ' r ) )
v
k
c
.
c
.
k
Kohn-Sham wave functions:
occ
v
k
v
k
v
k
n
(
r
)
occ
v
k
v
k
u
2 (
l
v
)
ion
(
u
r ) (
l
' )
v
k
d
3
r n
( r )
u
2 (
l
v
)
ion
u
( r ) (
l
' )
R el
0
occ
v
k
u
v
k (
l
)
v
ion u
(
l
( r ' ) )
v
k
c
.
c
.
d
3
r
n
( r )
u
(
l
)
v
ion
u
(
l
( ' r ) )
d
3 r
d
3 r '
v
ion u
(
l
( r ) ) ( r , r ' )
v
ion u
( (
l
r ' ' ) )
TH
1
T
Adiabatic condition Secular equation
M
2 Q
u c
H
1
T
u
(
R ion
R
0
el
TH
1
T
)
u
Non-local dielectric response (susceptibility)
H
1 ' (
l
,
l
' )
d
3
r d
3
r
Y
(
r
r
l
) (
r
,
r
)
Y
' (
r
r
l
' ' ).
Adiabatic dynamic electron density oscillations
n
(
r
,t
)
d
3
r
(
r
,
r
)
l
v ion
(
r
) /
r
l
u
(
l
,
t
)