Fishing Bosons in the depths of Fermi Sea Giorgio Benedek Università di Milano-Bicocca Pavia, 6 March 2014.

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

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

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

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

QQ

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?

|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

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...)

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