多重散乱法を用いたプラズモンロス計算の使用例

千葉大学
融合理工学府 先進理化学専攻 助教
二木かおり
17.09.25⟨ψ⃗− |∆|φi ⟩ =k≈!
α⃗α−i⃗k·Re! !

L1 ,L2 A,L3A
YL1 (k̂)[(1 − X)−1 ]α,AM
L2 ,L3
L1,L2

多重散乱理論 Multiple Scattering theory

Enable us to simulate the behavior of photoelectrons
Iｔ appropriate for considering theunoccupied states = continuum state= the behavior of photoelectron

1−−|ψ⃗ ⟩ = |φ⃗k ⟩ +V|ψ⟩⃗+kk
Ek − H0 − i0V (⃗r ) =!
α"⃗ α|vα |⃗r − R#Multiple Scattering theory

Enable us to simulate the behavior of photoelectrons
Is appropriate for considering the unoccupied states=continuum state= the behaviorof photoelectron

Partition the real space into atomic scattering regionsV (⃗r ) =!
α"

⃗ α|vα |⃗r − R#Photoelectron

X-ray

Apply Lipmann-Schwinger Eq. for final state|ψ⃗− ⟩ = |φ⃗k ⟩ +kScatterer α

1−V|ψ
⟩
⃗
k
Ek − H0 − i0+≈!
α⃗α−i⃗k·Re! !

L1 ,L2 A,L3

MLA2 ,L3A
YL1 (k̂)[(1 − X)−1 ]α,A
L1,L2 ML2 ,L3propagation / scattering

Initial state WF
・ Atomic WF
・ Molecular Orbital ( Gaussian )tαl1GαA
L1 ,L2A

Scattering amplitude⟨ψ⃗− |∆|φi ⟩ =kα

Scatterer A(absorber)

Potential

optical transition in atom A
Atomic scattering・ Radial integral
・ Phase shift

MS theory

Photoemission amplitude

Electronic state
Adsorbing effects

Our lab…

Full potentialPentacene

ARPES
Fe2O3 surface
Surface structure
Multiple
Magnetic anisotoropy

Scattering
theoryAmorphousmagnetic thin film

EXAFS
XMCD

To explore physicalproperties

Heusler alloy systems
Electrode of Li-ion battery科研費 若手BPlasmon loss

XPS
Metal
Thin Film （Graphene...)Nano particles,Today’s Topic

Satellite peaks in XPS; plasmon loss peaks
1. Expressions for plasmon loss intensity
which is called Quantum Landau formula.
2. Extension to other systems… graphene sheet and nano particles.

プラズモン
固体物質中での自由電子の集団振動
電荷分布のずれにより誘起される。
物質固有の共鳴振動数ωpをもつ。
表面局在プラズモン

表面伝播プラズモン
入射光

入射光
−−−
光の電場
++ +

バルクプラズモン
入射光＋＋＋ − − −

金属

ωp

ωp

√3

√2＋＋＋ − − −

金属

ωp

近接場光
ナノフォトニクス・プラズモニクスへの応用

XPS spectrum for Li

S. P. Kowalczyk et al., Phys. Rev. B 8, 3583 (1973).

7.3eV 7.5eV
57.2 eV64.7 eV
72 eV

Plasmon loss Main peak

I (p; w) + × × × ??
1c2(I (p; w) = 2p f D fc S 0 d E0 + w - E0* - e p0cp

Plasmon is collective electron oscillation excited by Δρ.
Plasmon loss peaks in XPS are observed due to excite the plasmon by photoelectron.

)
7

XPS spectrum for Li

S. P. Kowalczyk et al., Phys. Rev. B 8, 3583 (1973).

7.3eV 7.5eV
57.2 eV64.7 eV72 eVPlasmon

Plasmon loss Main peak

I (p; w) + × × × ??
1cΔρ2(I (p; w) = 2p f D fc S 0 d E0 + w - E0* - e p0cp

Plasmon is collective electron oscillation excited by Δρ.
Plasmon loss peaks in XPS are observed due to excite the plasmon by photoelectron.

)
8Plasmon Losses in XPSExtrinsic plasmon

Intrinsic plasmon（shake up）

X-ray

Photoelectron

Photoelectron

X-ray
damping

damping
damping

Photoelectron emission
Plasmon excitation

In solid

valence electrons

pote by no coremPhotoelectron emission

ExtIntI (p; w)1 = 2p å

Photoelectron induce
Plasmon excitationf p- D fc mv* 0*v + f p- vm g (e p + wm )D fc eloss propagation

干渉！！
The fluctuation potential

a22(´ d E0 + w - E0* - wm - e p)Extrinsic plasmon loss with the elastic scattering
T. Fujikawa, M. Kazama, H. Shinotsuka, e-J. Surf. Sci. Nanotech. 6 (2008) 263.

Photoelectron

X-rayTake account into the elastic scattering
during propagation for extrinsic termt ext (p ) = f vm g (e p + wm )D fc ep-Plasmon excitation(inelastic scattering)a2f ' p (1 + tg 0 )Βelastic scatteringAæ
öaç÷
rewrite the T-matrix= f 'p ç1 + t A g 0 + å ta g A + å t b g 0ta g A + !÷vm ( g A + å g 0t b g A + !)D fc e 2
a¹A
a ¹ A¹ bb¹A
using the site-T matrix
ç÷
b=Ag
=Aè
ø
The effect of scattering-a2= e { fp' (1 + t A g 0 ) vm g A D fc + fp' (1 + t A g 0 ) vm å g 0t B g A D fc + !
Without elastic scatterings= t mex ( p ) f p- D fc

B¹ A

Single scattering by atom Bg A = g 0 + g 0t A g 0

Quantum Landau formula For lower calculation costInt

I (p; w)1 = 2p åmExtf p- D fc mv* 0*v + f p- vm g (e p + wm )D fc eloss propagationt m ( P) = t mex ( P) +SmS0a22(´ d E0 + w - E0* - wm - e p

光電子がSubex()tpfp D fc S 0 固体中の原子に
stitute m散乱される影響
2*a (e )= å t m ( P) d (e - wm ) e = w + E - E - e00pem

Quantum Landau formula with full multiple scatteringuSingle loss：spectrum of one plasmon excitation
1I ( p, w ) =)f p D fc

Photo emission
Peak hight

2 a (e )é ¥ a (e ) ùexp ê ò0 deee úûëPlasmonExcitation

Shape ofloss function

nolmarization

Purpose

We calculate single-plasmon loss features associated with Li 1s photoemission
using the QLF that includes full multiple scatterings.
Calculation result

The schematic view of the calculation setup
Cylinder model
Photonenergy
170 eV

8.7

8Linearly
polarized

The energy ofphotoelectrons
from Li 1s
are about 100 eV.

Cylinder model
contains 52 atoms.

6.5

Calculated single-plasmon loss intensities excited from Li 1s
Depth profile of plasmon loss

detector- 5.23

3.5 AZA

X-ray

3layerpolarization- 8.725layerBcc
atom diameter 1.52 A

Photo electron emitted parallel to polarizationfrom Li 1s is effected by defocusing effect.

ZA

Distance between the surface to emitter

3rd and 5th layer are alsoemphasized due to the defocusing effect.

Info from only calculation!!

Li is light atom,
However we can’t neglect the effect of elastic scattering.

Expansion to other systems…低次元電子系
For metamaterials and photoelectronics devices

Observation of the low energy Π plasmon in a single layer graphene by charge doping
using EELS

ng

Control of the Π plasmon in a single layer graphene by charge doping
S. Y. Shin et al., APPLIED PHYSICS LETTERS 99, 082110 (2011).
On a single layer graphene (SLG)

・They report a Π plasmon excitationn = 1.2×1013 cm2 (naturally doped from the substrate).
・They find a low-energy Π plasmon excitation arising fromdoped electron density 1.2×1013 cm2corresponding to 0.44 eV above the Dirac point ED(additional chargetransfer from K to an SLG epitaxially grown on SiC).
・This low-energy plasmon arises from the collective excitation ofelectrons within the partially occupied π* conduction band.

n6H-SiC(0001)

EELS

a low-energy Π plasmon
Π plasmonn = 7×1013 cm2n = 1.2×1013 cm2
Ep is a primary electron beam energy,ΔΘ is an incident (scattered) angle.

Observationof theofΠ plasmonin a single layer
chargegraphene
doping using byEELS
Observationthe Π plasmon
in agraphene
singlebylayer
charge doping using XPS
Core-level spectra from graphene
P R B (91), 4, 045402 (2015).
Bo E. Sernelius
Experimental (µ-XPS) C 1s core-level spectrumof a suspended single graphene sheet on a gold sheet
using the photon energy 480 eV.
For an doped
3.2×1013

experimentcalculation

They calculate singularity indices in pristine and doped grapheneusing dynamically screened Coulomb interaction
in doped graphene.
5×1013

1×1013

calculation

We can not see sharp a plasmon loss peak due to singularity
even if increasing doping.

calculation
We can see sharp plasmon loss peaks with doping.
P R B , 88, 245416 (2013).

We want to extract a information about from singularity.
extent to electron-hole pair, excitation near fermi level….. Collaborate with Rennes uni. based on JASSO.

Normalized Intensity〇キャリア密度依存性・hν = 450 eV条件
𝑛 = 1.0×10.. , 10.0 , 10.1 , 10.2 , 10.3 cm60の場合のそれぞれ計算

1.0

ピーク位置のシフトはほとんどない→密度依存性は現れない

0.80.60.4

密度が高いほど高ロスエネルギー側に裾の長いピークになる→キャリア密度がプラズモン分散に関与

0.20.00.1

0.08

0.06

0.04

Loss Energy [eV]0.020.0まとめ
量子ランダウ方程式からメインピークのサテライトピークである
プラズモンロスピークが計算できる
単純金属、2次元電子系グラフェン、0次元電子系のナノ粒子などへの拡張が見込まれる