nanoplasmonics within time-dependent density … · outline nanoplasmonics methods and computations...
TRANSCRIPT
![Page 1: Nanoplasmonics within time-dependent density … · Outline Nanoplasmonics Methods and computations Analyzing the plasmonic response Case studies In this talk: Finite systems For](https://reader031.vdocuments.site/reader031/viewer/2022013117/5b082fdf7f8b9a3d018bce36/html5/thumbnails/1.jpg)
Nanoplasmonics within
time-dependent density-functional theory
Tuomas Rossi
COMP Centre of ExcellenceDepartment of Applied Physics
Aalto University
GPAW 2016: Users and developers meeting
Jyväskylä
Wednesday 8th June 2016
tuomas.rossi aalto.fi
![Page 2: Nanoplasmonics within time-dependent density … · Outline Nanoplasmonics Methods and computations Analyzing the plasmonic response Case studies In this talk: Finite systems For](https://reader031.vdocuments.site/reader031/viewer/2022013117/5b082fdf7f8b9a3d018bce36/html5/thumbnails/2.jpg)
Outline
Nanoplasmonics
Methods and computations
Analyzing the plasmonic response
Case studies
Tuomas Rossi / tuomas.rossi aalto.fi / GPAW 2016 / Jyväskylä 2/47
![Page 3: Nanoplasmonics within time-dependent density … · Outline Nanoplasmonics Methods and computations Analyzing the plasmonic response Case studies In this talk: Finite systems For](https://reader031.vdocuments.site/reader031/viewer/2022013117/5b082fdf7f8b9a3d018bce36/html5/thumbnails/3.jpg)
Outline
Nanoplasmonics
Methods and computations
Analyzing the plasmonic response
Case studies
In this talk: Finite systems
For extended systems, seeK. Andersen, Quantum theory of plasmons in nanostructures, PhD thesis (2015).
Tuomas Rossi / tuomas.rossi aalto.fi / GPAW 2016 / Jyväskylä 2/47
![Page 4: Nanoplasmonics within time-dependent density … · Outline Nanoplasmonics Methods and computations Analyzing the plasmonic response Case studies In this talk: Finite systems For](https://reader031.vdocuments.site/reader031/viewer/2022013117/5b082fdf7f8b9a3d018bce36/html5/thumbnails/4.jpg)
Outline
Nanoplasmonics
Methods and computations
Analyzing the plasmonic response
Case studies
Tuomas Rossi / tuomas.rossi aalto.fi / GPAW 2016 / Jyväskylä 3/47
![Page 5: Nanoplasmonics within time-dependent density … · Outline Nanoplasmonics Methods and computations Analyzing the plasmonic response Case studies In this talk: Finite systems For](https://reader031.vdocuments.site/reader031/viewer/2022013117/5b082fdf7f8b9a3d018bce36/html5/thumbnails/5.jpg)
Localized surface plasmonCollective oscillation of valence electrons
◮ Plenty of applications◮ Light confinement◮ Spectroscopy◮ Biomedicine◮ . . .
Plasmon resonance
◮ strong
◮ enhanced field
◮ tunable by◮ shape◮ composition◮ environment
Tuomas Rossi / tuomas.rossi aalto.fi / GPAW 2016 / Jyväskylä 4/47
![Page 6: Nanoplasmonics within time-dependent density … · Outline Nanoplasmonics Methods and computations Analyzing the plasmonic response Case studies In this talk: Finite systems For](https://reader031.vdocuments.site/reader031/viewer/2022013117/5b082fdf7f8b9a3d018bce36/html5/thumbnails/6.jpg)
Plasmon coupling
Coupled plasmon modes (dipole-active):
Tuomas Rossi / tuomas.rossi aalto.fi / GPAW 2016 / Jyväskylä 5/47
![Page 7: Nanoplasmonics within time-dependent density … · Outline Nanoplasmonics Methods and computations Analyzing the plasmonic response Case studies In this talk: Finite systems For](https://reader031.vdocuments.site/reader031/viewer/2022013117/5b082fdf7f8b9a3d018bce36/html5/thumbnails/7.jpg)
Plasmon coupling
Coupled plasmon modes (dipole-active):
Tuomas Rossi / tuomas.rossi aalto.fi / GPAW 2016 / Jyväskylä 5/47
![Page 8: Nanoplasmonics within time-dependent density … · Outline Nanoplasmonics Methods and computations Analyzing the plasmonic response Case studies In this talk: Finite systems For](https://reader031.vdocuments.site/reader031/viewer/2022013117/5b082fdf7f8b9a3d018bce36/html5/thumbnails/8.jpg)
Nanoplasmonics
Tuomas Rossi / tuomas.rossi aalto.fi / GPAW 2016 / Jyväskylä 6/47
![Page 9: Nanoplasmonics within time-dependent density … · Outline Nanoplasmonics Methods and computations Analyzing the plasmonic response Case studies In this talk: Finite systems For](https://reader031.vdocuments.site/reader031/viewer/2022013117/5b082fdf7f8b9a3d018bce36/html5/thumbnails/9.jpg)
Nanoplasmonics
Small-size/quantum effects
◮ Tunneling
J. Zuloaga et al., Nano Lett. 9, 887 (2009)
K. J. Savage et al., Nature 491, 574 (2012)
J. A. Scholl et al., Nano Lett. 13, 564 (2013)
Tuomas Rossi / tuomas.rossi aalto.fi / GPAW 2016 / Jyväskylä 6/47
![Page 10: Nanoplasmonics within time-dependent density … · Outline Nanoplasmonics Methods and computations Analyzing the plasmonic response Case studies In this talk: Finite systems For](https://reader031.vdocuments.site/reader031/viewer/2022013117/5b082fdf7f8b9a3d018bce36/html5/thumbnails/10.jpg)
Nanoplasmonics
Small-size/quantum effects
◮ Tunneling
◮ Atomistic details
P. Zhang et al., Phys. Rev. B 90, 161407(R) (2014)
M. Barbry et al., Nano Lett. 15, 3410 (2015)
A. Varas et al., J. Phys. Chem. Lett. 6, 1891 (2015)
Tuomas Rossi / tuomas.rossi aalto.fi / GPAW 2016 / Jyväskylä 6/47
![Page 11: Nanoplasmonics within time-dependent density … · Outline Nanoplasmonics Methods and computations Analyzing the plasmonic response Case studies In this talk: Finite systems For](https://reader031.vdocuments.site/reader031/viewer/2022013117/5b082fdf7f8b9a3d018bce36/html5/thumbnails/11.jpg)
Nanoplasmonics
Small-size/quantum effects
◮ Tunneling
◮ Atomistic details
◮ Molecular junctions
P. Song et al., J. Chem. Phys. 134, 074701 (2011)
P. Song et al., Phys. Rev. B 86, 121410 (2012)
S. F. Tan et al., Science 343, 1496 (2014)
V. Kulkarni and A. Manjavacas, ACS Photonics 2, 987 (2015)
Tuomas Rossi / tuomas.rossi aalto.fi / GPAW 2016 / Jyväskylä 6/47
![Page 12: Nanoplasmonics within time-dependent density … · Outline Nanoplasmonics Methods and computations Analyzing the plasmonic response Case studies In this talk: Finite systems For](https://reader031.vdocuments.site/reader031/viewer/2022013117/5b082fdf7f8b9a3d018bce36/html5/thumbnails/12.jpg)
Nanoplasmonics
Small-size/quantum effects
◮ Tunneling
◮ Atomistic details
◮ Molecular junctions
◮ Case study:
quantum transport
through nanocontact
Tuomas Rossi / tuomas.rossi aalto.fi / GPAW 2016 / Jyväskylä 6/47
![Page 13: Nanoplasmonics within time-dependent density … · Outline Nanoplasmonics Methods and computations Analyzing the plasmonic response Case studies In this talk: Finite systems For](https://reader031.vdocuments.site/reader031/viewer/2022013117/5b082fdf7f8b9a3d018bce36/html5/thumbnails/13.jpg)
Outline
Nanoplasmonics
Methods and computations
Time-dependent density-functional theory (TDDFT)
Time-propagation TDDFT with localized basis
Hybrid quantum–classical scheme
Practical aspects
Analyzing the plasmonic response
Case studies
Tuomas Rossi / tuomas.rossi aalto.fi / GPAW 2016 / Jyväskylä 7/47
![Page 14: Nanoplasmonics within time-dependent density … · Outline Nanoplasmonics Methods and computations Analyzing the plasmonic response Case studies In this talk: Finite systems For](https://reader031.vdocuments.site/reader031/viewer/2022013117/5b082fdf7f8b9a3d018bce36/html5/thumbnails/14.jpg)
Outline
Nanoplasmonics
Methods and computations
Time-dependent density-functional theory (TDDFT)
Time-propagation TDDFT with localized basis
Hybrid quantum–classical scheme
Practical aspects
Analyzing the plasmonic response
Case studies
Tuomas Rossi / tuomas.rossi aalto.fi / GPAW 2016 / Jyväskylä 8/47
![Page 15: Nanoplasmonics within time-dependent density … · Outline Nanoplasmonics Methods and computations Analyzing the plasmonic response Case studies In this talk: Finite systems For](https://reader031.vdocuments.site/reader031/viewer/2022013117/5b082fdf7f8b9a3d018bce36/html5/thumbnails/15.jpg)
Time-dependent density-functional theory
DFT: The ground-state electronic structure
H[n]ψj(r) = ǫjψj(r), j = 1, . . . ,N
TDDFT: The time-evolution/response of the system at the initial
state {ψj(r , t = 0) = ψ0j (r)}
H[n](t)ψj(r , t) = i∂
∂tψj(r , t)
Kohn-Sham Hamiltonian
H[n](t) = −1
2∇2 +
∫
n(r ′, t)
|r − r ′|dr + vext(r , t) + vxc[n](r , t)
Adiabatic approximation: vxc[n](r , t) = vxc[n(t)](r) (no memory)
{ψj}
n
H
E. Runge and E. K. U. Gross, Phys. Rev. Lett. 52, 997 (1984).doi:10.1103/PhysRevLett.52.997
Tuomas Rossi / tuomas.rossi aalto.fi / GPAW 2016 / Jyväskylä 9/47
![Page 16: Nanoplasmonics within time-dependent density … · Outline Nanoplasmonics Methods and computations Analyzing the plasmonic response Case studies In this talk: Finite systems For](https://reader031.vdocuments.site/reader031/viewer/2022013117/5b082fdf7f8b9a3d018bce36/html5/thumbnails/16.jpg)
TDDFT in GPAW
Solve time-dependent equations by
◮ Real-time propagation (full non-linear response) or◮ from gpaw.tddft import TDDFT◮ from gpaw.lcaotddft import LCAOTDDFT
◮ Linear response in frequency space (sum over states)◮ from gpaw.lrtddft import LrTDDFT◮ from gpaw.lrtddft2 import LrTDDFT2
Note: also extended systems!
◮ from gpaw.response.df import DielectricFunction
(But in this talk the focus on finite systems!)
Tuomas Rossi / tuomas.rossi aalto.fi / GPAW 2016 / Jyväskylä 10/47
![Page 17: Nanoplasmonics within time-dependent density … · Outline Nanoplasmonics Methods and computations Analyzing the plasmonic response Case studies In this talk: Finite systems For](https://reader031.vdocuments.site/reader031/viewer/2022013117/5b082fdf7f8b9a3d018bce36/html5/thumbnails/17.jpg)
Outline
Nanoplasmonics
Methods and computations
Time-dependent density-functional theory (TDDFT)
Time-propagation TDDFT with localized basis
Hybrid quantum–classical scheme
Practical aspects
Analyzing the plasmonic response
Case studies
Tuomas Rossi / tuomas.rossi aalto.fi / GPAW 2016 / Jyväskylä 11/47
![Page 18: Nanoplasmonics within time-dependent density … · Outline Nanoplasmonics Methods and computations Analyzing the plasmonic response Case studies In this talk: Finite systems For](https://reader031.vdocuments.site/reader031/viewer/2022013117/5b082fdf7f8b9a3d018bce36/html5/thumbnails/18.jpg)
Recipe for time-propagation TDDFT
1. Calculate the ground state◮ ground state wave functions
2. “Kick” with a delta-pulse of light(linear regime)
◮ dipole approximation:
δvext(r , t) = r · Eextδ(t)
3. Propagate the wave functions in time◮ record the quantities of interest
(density, dipole moment)
4. Analyze◮ Fourier transform
E(t)
light
0 5 10 15 20 25 30Time (fs)
6420246
Dip
ole
mom
ent
0 1 2 3 4 5 6Energy (eV)
64202468
10
Pola
riza
bili
ty
Re
Im
K. Yabana and G. F. Bertsch, Phys. Rev. B 54, 4484 (1996).doi:10.1103/PhysRevB.54.4484
Tuomas Rossi / tuomas.rossi aalto.fi / GPAW 2016 / Jyväskylä 12/47
![Page 19: Nanoplasmonics within time-dependent density … · Outline Nanoplasmonics Methods and computations Analyzing the plasmonic response Case studies In this talk: Finite systems For](https://reader031.vdocuments.site/reader031/viewer/2022013117/5b082fdf7f8b9a3d018bce36/html5/thumbnails/19.jpg)
Localized basis sets (LCAO)
Represent the wave functions as linear combinations of atomic
orbitals/atom-localized functions (LCAO)
χai (r) = φa
n,l(r)Y ml (θ, ϕ)
0 2 4 6 8 10
r (Bohr)
0.0
0.2
0.4
0.6
0.8
1.0
Basis
fu
ncti
on
(arb
. u
.)
4d-sz confined orbital
4d-dz split-valence function
5s-sz confined orbital
5s-dz split-valence function
p-type Gaussian polarization
s
p
d
f
dzp basis
Tuomas Rossi / tuomas.rossi aalto.fi / GPAW 2016 / Jyväskylä 13/47
![Page 20: Nanoplasmonics within time-dependent density … · Outline Nanoplasmonics Methods and computations Analyzing the plasmonic response Case studies In this talk: Finite systems For](https://reader031.vdocuments.site/reader031/viewer/2022013117/5b082fdf7f8b9a3d018bce36/html5/thumbnails/20.jpg)
LCAO – Highly efficient calculations
Recent LCAO-TDDFT implementation in GPAW
◮ from gpaw.lcaotddft import LCAOTDDFT
Absorp
tion / a
tom
(arb
. units)
Energy (eV)
(a)
Ag55 Ico
Ag147 Ico
Ag309 Ico
Ag561 Ico
QS Sph
QS Ico
Ag147 PBE Ico
3 3.2 3.4 3.6 3.8 4 4.2 4.4
LS
PR
energ
y (
eV
)
1/D (nm−1
)
(b)
TDDFT Ico
Exp.
QS Sph
QS Ico
0.0 0.5 1.0
3.4
3.6
3.8
4
4.2
4.4
4.6
M. Kuisma, A. Sakko, T. P. Rossi, A. H. Larsen, J. Enkovaara, L. Lehtovaara, andT. T. Rantala, Phys. Rev. B 91, 115431 (2015). doi:10.1103/PhysRevB.91.115431
Tuomas Rossi / tuomas.rossi aalto.fi / GPAW 2016 / Jyväskylä 14/47
![Page 21: Nanoplasmonics within time-dependent density … · Outline Nanoplasmonics Methods and computations Analyzing the plasmonic response Case studies In this talk: Finite systems For](https://reader031.vdocuments.site/reader031/viewer/2022013117/5b082fdf7f8b9a3d018bce36/html5/thumbnails/21.jpg)
LCAO – . . . but no simple convergence parameters
Default basis sets (designed for DFT ground-state-energy
calculations) may not be suitable for response calculations
How to extend the basis sets?
◮ Generate functions based on atomic orbitals (e.g.,
split-valence)
◮ Use some general function form (e.g., Gaussian)
Tuomas Rossi / tuomas.rossi aalto.fi / GPAW 2016 / Jyväskylä 15/47
![Page 22: Nanoplasmonics within time-dependent density … · Outline Nanoplasmonics Methods and computations Analyzing the plasmonic response Case studies In this talk: Finite systems For](https://reader031.vdocuments.site/reader031/viewer/2022013117/5b082fdf7f8b9a3d018bce36/html5/thumbnails/22.jpg)
LCAO – pvalence basis sets
Replace the default p-type polarization function with diffuse 5p
unoccupied orbital (and its split-valence function)
0 2 4 6 8 10r (Bohr)
0.0
0.2
0.4
0.6
0.8
1.0
Basis
func
tion (
arb. u
.) (a)Default DZP basis
4d-sz confined orbital 4d-dz split-valence function 5s-sz confined orbital 5s-dz split-valence function p-type Gaussian polarization
0 2 4 6 8 10r (Bohr)
(b)Optimized DZ basis with 5p functions
4d-sz confined orbital 4d-dz split-valence function 5s-sz confined orbital 5s-dz split-valence function 5p-sz confined orbital 5p-dz split-valence function
M. Kuisma, A. Sakko, T. P. Rossi, A. H. Larsen, J. Enkovaara, L. Lehtovaara, andT. T. Rantala, Phys. Rev. B 91, 115431 (2015). doi:10.1103/PhysRevB.91.115431
Tuomas Rossi / tuomas.rossi aalto.fi / GPAW 2016 / Jyväskylä 16/47
![Page 23: Nanoplasmonics within time-dependent density … · Outline Nanoplasmonics Methods and computations Analyzing the plasmonic response Case studies In this talk: Finite systems For](https://reader031.vdocuments.site/reader031/viewer/2022013117/5b082fdf7f8b9a3d018bce36/html5/thumbnails/23.jpg)
LCAO – pvalence basis sets
Replace the default p-type polarization function with diffuse 5p
unoccupied orbital (and its split-valence function)
Generated for all suitable elements, available in GPAW:
gpaw install-data <dir> --basis --version=pvalence
M. Kuisma, A. Sakko, T. P. Rossi, A. H. Larsen, J. Enkovaara, L. Lehtovaara, andT. T. Rantala, Phys. Rev. B 91, 115431 (2015). doi:10.1103/PhysRevB.91.115431
Tuomas Rossi / tuomas.rossi aalto.fi / GPAW 2016 / Jyväskylä 16/47
![Page 24: Nanoplasmonics within time-dependent density … · Outline Nanoplasmonics Methods and computations Analyzing the plasmonic response Case studies In this talk: Finite systems For](https://reader031.vdocuments.site/reader031/viewer/2022013117/5b082fdf7f8b9a3d018bce36/html5/thumbnails/24.jpg)
Completeness-optimization: NAO+NGTO basis sets
Augment atomic-orbital (NAO) basis set with numerical
Gaussian-type orbitals (NGTOs)
◮ NGTOs selected by systematic completeness-optimization
of the spectrum of the atomic dimer (e.g., Ag2)
T. P. Rossi, S. Lehtola, A. Sakko, M. J. Puska, and R. M. Nieminen,J. Chem. Phys. 142, 094114 (2015). doi:10.1063/1.4913739
Tuomas Rossi / tuomas.rossi aalto.fi / GPAW 2016 / Jyväskylä 17/47
![Page 25: Nanoplasmonics within time-dependent density … · Outline Nanoplasmonics Methods and computations Analyzing the plasmonic response Case studies In this talk: Finite systems For](https://reader031.vdocuments.site/reader031/viewer/2022013117/5b082fdf7f8b9a3d018bce36/html5/thumbnails/25.jpg)
Co-optimized NAO+NGTO – coopt basis sets
The obtained basis sets are transferable to larger systems
Generated for Cu, Ag, and Au, available in GPAW:
gpaw install-data <dir> --basis --version=coopt
T. P. Rossi, S. Lehtola, A. Sakko, M. J. Puska, and R. M. Nieminen,J. Chem. Phys. 142, 094114 (2015). doi:10.1063/1.4913739
Tuomas Rossi / tuomas.rossi aalto.fi / GPAW 2016 / Jyväskylä 18/47
![Page 26: Nanoplasmonics within time-dependent density … · Outline Nanoplasmonics Methods and computations Analyzing the plasmonic response Case studies In this talk: Finite systems For](https://reader031.vdocuments.site/reader031/viewer/2022013117/5b082fdf7f8b9a3d018bce36/html5/thumbnails/26.jpg)
Outline
Nanoplasmonics
Methods and computations
Time-dependent density-functional theory (TDDFT)
Time-propagation TDDFT with localized basis
Hybrid quantum–classical scheme
Practical aspects
Analyzing the plasmonic response
Case studies
Tuomas Rossi / tuomas.rossi aalto.fi / GPAW 2016 / Jyväskylä 19/47
![Page 27: Nanoplasmonics within time-dependent density … · Outline Nanoplasmonics Methods and computations Analyzing the plasmonic response Case studies In this talk: Finite systems For](https://reader031.vdocuments.site/reader031/viewer/2022013117/5b082fdf7f8b9a3d018bce36/html5/thumbnails/27.jpg)
Hybrid quantum–classical scheme
Idea: separate the system to quantum and classical parts
Quantum part (e.g., a molecule):
◮ Time-propagation TDDFT
Classical part (e.g., a large nanoparticle):
◮ Describe material with (experimentally measured)
permittivity ǫ(ω)
◮ Solve Maxwell’s equations at the quasistatic description by
time-propagation
Coupling
◮ The potential ∇2V tot(r , t) = −4π[ρcl(r , t) + ρqm(r , t)]
from gpaw.fdtd.poisson_fdtd import QSFDTD
A. Sakko, T. P. Rossi, and R. M. Nieminen, J. Phys.: Condens. Matter 26, 315013 (2014).doi:10.1088/0953-8984/26/28/315013
Tuomas Rossi / tuomas.rossi aalto.fi / GPAW 2016 / Jyväskylä 20/47
![Page 28: Nanoplasmonics within time-dependent density … · Outline Nanoplasmonics Methods and computations Analyzing the plasmonic response Case studies In this talk: Finite systems For](https://reader031.vdocuments.site/reader031/viewer/2022013117/5b082fdf7f8b9a3d018bce36/html5/thumbnails/28.jpg)
Hybrid quantum–classical scheme: Example
A. Sakko, T. P. Rossi, and R. M. Nieminen, J. Phys.: Condens. Matter 26, 315013 (2014).doi:10.1088/0953-8984/26/28/315013
Tuomas Rossi / tuomas.rossi aalto.fi / GPAW 2016 / Jyväskylä 21/47
![Page 29: Nanoplasmonics within time-dependent density … · Outline Nanoplasmonics Methods and computations Analyzing the plasmonic response Case studies In this talk: Finite systems For](https://reader031.vdocuments.site/reader031/viewer/2022013117/5b082fdf7f8b9a3d018bce36/html5/thumbnails/29.jpg)
Outline
Nanoplasmonics
Methods and computations
Time-dependent density-functional theory (TDDFT)
Time-propagation TDDFT with localized basis
Hybrid quantum–classical scheme
Practical aspects
Analyzing the plasmonic response
Case studies
Tuomas Rossi / tuomas.rossi aalto.fi / GPAW 2016 / Jyväskylä 22/47
![Page 30: Nanoplasmonics within time-dependent density … · Outline Nanoplasmonics Methods and computations Analyzing the plasmonic response Case studies In this talk: Finite systems For](https://reader031.vdocuments.site/reader031/viewer/2022013117/5b082fdf7f8b9a3d018bce36/html5/thumbnails/30.jpg)
Poisson equation
Problem
◮ Charge oscillation at plasmonic resonance induces strong
global dipole
→ Small cell with zero boundary conditions for potential is
not ok!
Solution
◮ Use multipole moment corrections
◮ Calculate potential on an extended grid
Tuomas Rossi / tuomas.rossi aalto.fi / GPAW 2016 / Jyväskylä 23/47
![Page 31: Nanoplasmonics within time-dependent density … · Outline Nanoplasmonics Methods and computations Analyzing the plasmonic response Case studies In this talk: Finite systems For](https://reader031.vdocuments.site/reader031/viewer/2022013117/5b082fdf7f8b9a3d018bce36/html5/thumbnails/31.jpg)
Poisson equation: illustration
0.4 0.2 0.0 0.2 0.4z coordinate
0.020
0.015
0.010
0.005
0.000
0.005
0.010
0.015
0.020
Dens
ity
ρ
0.4 0.2 0.0 0.2 0.4z coordinate
0.0015
0.0010
0.0005
0.0000
0.0005
0.0010
0.0015
Pote
ntia
l
v (direct)
Tuomas Rossi / tuomas.rossi aalto.fi / GPAW 2016 / Jyväskylä 24/47
![Page 32: Nanoplasmonics within time-dependent density … · Outline Nanoplasmonics Methods and computations Analyzing the plasmonic response Case studies In this talk: Finite systems For](https://reader031.vdocuments.site/reader031/viewer/2022013117/5b082fdf7f8b9a3d018bce36/html5/thumbnails/32.jpg)
Poisson equation: illustration
0.4 0.2 0.0 0.2 0.4z coordinate
0.020
0.015
0.010
0.005
0.000
0.005
0.010
0.015
0.020
Dens
ity
ρ
0.4 0.2 0.0 0.2 0.4z coordinate
0.0015
0.0010
0.0005
0.0000
0.0005
0.0010
0.0015
Pote
ntia
l
v (direct)v (direct on extended grid)
Tuomas Rossi / tuomas.rossi aalto.fi / GPAW 2016 / Jyväskylä 24/47
![Page 33: Nanoplasmonics within time-dependent density … · Outline Nanoplasmonics Methods and computations Analyzing the plasmonic response Case studies In this talk: Finite systems For](https://reader031.vdocuments.site/reader031/viewer/2022013117/5b082fdf7f8b9a3d018bce36/html5/thumbnails/33.jpg)
Poisson equation: illustration
0.4 0.2 0.0 0.2 0.4z coordinate
0.020
0.015
0.010
0.005
0.000
0.005
0.010
0.015
0.020
Dens
ity
ρ
ρc
ρ+ρc
0.4 0.2 0.0 0.2 0.4z coordinate
0.0015
0.0010
0.0005
0.0000
0.0005
0.0010
0.0015
Pote
ntia
l
v (direct)v (direct on extended grid)v+vc
−vcv
Tuomas Rossi / tuomas.rossi aalto.fi / GPAW 2016 / Jyväskylä 24/47
![Page 34: Nanoplasmonics within time-dependent density … · Outline Nanoplasmonics Methods and computations Analyzing the plasmonic response Case studies In this talk: Finite systems For](https://reader031.vdocuments.site/reader031/viewer/2022013117/5b082fdf7f8b9a3d018bce36/html5/thumbnails/34.jpg)
PoissonSolver zooMultipole moment correctionsfrom gpaw.poisson import PoissonSolver
PoissonSolver(eps=1e-20, remove_moment=1+3+5)
◮ For ∼ spherical systems (or spherical unit cells)
Multiple multipole moment correctionsfrom gpaw.poisson_extended import ExtendedPoissonSolver
moment_corrections = [{’moms’: moments, ’center’: center1},
{’moms’: moments, ’center’: center2},
...]
ExtendedPoissonSolver(eps=1e-20, moment_corrections=moment_corrections)
◮ For nanoparticle dimer, trimer, . . .
Calculate potential on an extended grid
ExtendedPoissonSolver(eps=1e-20, extended={’gpts’: (512, 256, 256)})
◮ For general cases
Tuomas Rossi / tuomas.rossi aalto.fi / GPAW 2016 / Jyväskylä 25/47
![Page 35: Nanoplasmonics within time-dependent density … · Outline Nanoplasmonics Methods and computations Analyzing the plasmonic response Case studies In this talk: Finite systems For](https://reader031.vdocuments.site/reader031/viewer/2022013117/5b082fdf7f8b9a3d018bce36/html5/thumbnails/35.jpg)
Outline
Nanoplasmonics
Methods and computations
Analyzing the plasmonic response
Spectra
Real-space quantities
Spatially resolved spectra
Electron transitions
Case studies
Tuomas Rossi / tuomas.rossi aalto.fi / GPAW 2016 / Jyväskylä 26/47
![Page 36: Nanoplasmonics within time-dependent density … · Outline Nanoplasmonics Methods and computations Analyzing the plasmonic response Case studies In this talk: Finite systems For](https://reader031.vdocuments.site/reader031/viewer/2022013117/5b082fdf7f8b9a3d018bce36/html5/thumbnails/36.jpg)
Outline
Nanoplasmonics
Methods and computations
Analyzing the plasmonic response
Spectra
Real-space quantities
Spatially resolved spectra
Electron transitions
Case studies
Tuomas Rossi / tuomas.rossi aalto.fi / GPAW 2016 / Jyväskylä 27/47
![Page 37: Nanoplasmonics within time-dependent density … · Outline Nanoplasmonics Methods and computations Analyzing the plasmonic response Case studies In this talk: Finite systems For](https://reader031.vdocuments.site/reader031/viewer/2022013117/5b082fdf7f8b9a3d018bce36/html5/thumbnails/37.jpg)
Photoabsoprtion and polarizability
α(ω) =δµ(ω)
E0
S(ω) =2ω
πIm[α(ω)]
Kramers-Kronig relations
Tuomas Rossi / tuomas.rossi aalto.fi / GPAW 2016 / Jyväskylä 28/47
![Page 38: Nanoplasmonics within time-dependent density … · Outline Nanoplasmonics Methods and computations Analyzing the plasmonic response Case studies In this talk: Finite systems For](https://reader031.vdocuments.site/reader031/viewer/2022013117/5b082fdf7f8b9a3d018bce36/html5/thumbnails/38.jpg)
Outline
Nanoplasmonics
Methods and computations
Analyzing the plasmonic response
Spectra
Real-space quantities
Spatially resolved spectra
Electron transitions
Case studies
Tuomas Rossi / tuomas.rossi aalto.fi / GPAW 2016 / Jyväskylä 29/47
![Page 39: Nanoplasmonics within time-dependent density … · Outline Nanoplasmonics Methods and computations Analyzing the plasmonic response Case studies In this talk: Finite systems For](https://reader031.vdocuments.site/reader031/viewer/2022013117/5b082fdf7f8b9a3d018bce36/html5/thumbnails/39.jpg)
Induced density
Tuomas Rossi / tuomas.rossi aalto.fi / GPAW 2016 / Jyväskylä 30/47
![Page 40: Nanoplasmonics within time-dependent density … · Outline Nanoplasmonics Methods and computations Analyzing the plasmonic response Case studies In this talk: Finite systems For](https://reader031.vdocuments.site/reader031/viewer/2022013117/5b082fdf7f8b9a3d018bce36/html5/thumbnails/40.jpg)
Induced density
Absorp
tion / a
tom
(arb
. units)
Energy (eV)
(a)
Ag55 Ico
Ag147 Ico
Ag309 Ico
Ag561 Ico
QS Sph
QS Ico
Ag147 PBE Ico
3 3.2 3.4 3.6 3.8 4 4.2 4.4
LS
PR
energ
y (
eV
)
1/D (nm−1
)
(b)
TDDFT Ico
Exp.
QS Sph
QS Ico
0.0 0.5 1.0
3.4
3.6
3.8
4
4.2
4.4
4.6
M. Kuisma, A. Sakko, T. P. Rossi, A. H. Larsen, J. Enkovaara, L. Lehtovaara, andT. T. Rantala, Phys. Rev. B 91, 115431 (2015). doi:10.1103/PhysRevB.91.115431
Tuomas Rossi / tuomas.rossi aalto.fi / GPAW 2016 / Jyväskylä 31/47
![Page 41: Nanoplasmonics within time-dependent density … · Outline Nanoplasmonics Methods and computations Analyzing the plasmonic response Case studies In this talk: Finite systems For](https://reader031.vdocuments.site/reader031/viewer/2022013117/5b082fdf7f8b9a3d018bce36/html5/thumbnails/41.jpg)
Induced density → potential → electric near field
from gpaw.inducedfield.inducedfield_tddft import TDDFTInducedField
Tuomas Rossi / tuomas.rossi aalto.fi / GPAW 2016 / Jyväskylä 32/47
![Page 42: Nanoplasmonics within time-dependent density … · Outline Nanoplasmonics Methods and computations Analyzing the plasmonic response Case studies In this talk: Finite systems For](https://reader031.vdocuments.site/reader031/viewer/2022013117/5b082fdf7f8b9a3d018bce36/html5/thumbnails/42.jpg)
Outline
Nanoplasmonics
Methods and computations
Analyzing the plasmonic response
Spectra
Real-space quantities
Spatially resolved spectra
Electron transitions
Case studies
Tuomas Rossi / tuomas.rossi aalto.fi / GPAW 2016 / Jyväskylä 33/47
![Page 43: Nanoplasmonics within time-dependent density … · Outline Nanoplasmonics Methods and computations Analyzing the plasmonic response Case studies In this talk: Finite systems For](https://reader031.vdocuments.site/reader031/viewer/2022013117/5b082fdf7f8b9a3d018bce36/html5/thumbnails/43.jpg)
Integrated induced density map
δρ̃(z, ω) = Im
[∫
δρ(r , ω) dxdy
]
S(ω) ∝ ω
∫
z δρ̃(z, ω) dz
T. P. Rossi, A. Zugarramurdi, M. J. Puska, and R. M. Nieminen,Phys. Rev. Lett. 115, 236804 (2015). doi:10.1103/PhysRevLett.115.236804
Tuomas Rossi / tuomas.rossi aalto.fi / GPAW 2016 / Jyväskylä 34/47
![Page 44: Nanoplasmonics within time-dependent density … · Outline Nanoplasmonics Methods and computations Analyzing the plasmonic response Case studies In this talk: Finite systems For](https://reader031.vdocuments.site/reader031/viewer/2022013117/5b082fdf7f8b9a3d018bce36/html5/thumbnails/44.jpg)
Outline
Nanoplasmonics
Methods and computations
Analyzing the plasmonic response
Spectra
Real-space quantities
Spatially resolved spectra
Electron transitions
Case studies
Tuomas Rossi / tuomas.rossi aalto.fi / GPAW 2016 / Jyväskylä 35/47
![Page 45: Nanoplasmonics within time-dependent density … · Outline Nanoplasmonics Methods and computations Analyzing the plasmonic response Case studies In this talk: Finite systems For](https://reader031.vdocuments.site/reader031/viewer/2022013117/5b082fdf7f8b9a3d018bce36/html5/thumbnails/45.jpg)
Kohn–Sham decomposition
Small systems:
List transitions
H2O
E=8.065 eV, f=0.031533
3->4 u 0.99986
0->8 u 0.00013
rest=1.57e-16
Tuomas Rossi / tuomas.rossi aalto.fi / GPAW 2016 / Jyväskylä 36/47
![Page 46: Nanoplasmonics within time-dependent density … · Outline Nanoplasmonics Methods and computations Analyzing the plasmonic response Case studies In this talk: Finite systems For](https://reader031.vdocuments.site/reader031/viewer/2022013117/5b082fdf7f8b9a3d018bce36/html5/thumbnails/46.jpg)
Kohn–Sham decomposition
Small systems:
List transitions
H2O
E=8.065 eV, f=0.031533
3->4 u 0.99986
0->8 u 0.00013
rest=1.57e-16
Large systems:
Transition contribution map
S. Malola, L. Lehtovaara, J. Enkovaara, and H. Häkkinen, ACS Nano 7, 10263 (2013).doi:10.1021/nn4046634
Tuomas Rossi / tuomas.rossi aalto.fi / GPAW 2016 / Jyväskylä 36/47
![Page 47: Nanoplasmonics within time-dependent density … · Outline Nanoplasmonics Methods and computations Analyzing the plasmonic response Case studies In this talk: Finite systems For](https://reader031.vdocuments.site/reader031/viewer/2022013117/5b082fdf7f8b9a3d018bce36/html5/thumbnails/47.jpg)
Kohn–Sham decomposition
Small systems:
List transitions
H2O
E=8.065 eV, f=0.031533
3->4 u 0.99986
0->8 u 0.00013
rest=1.57e-16
Large systems:
Transition contribution map
S. Malola, L. Lehtovaara, J. Enkovaara, and H. Häkkinen, ACS Nano 7, 10263 (2013).doi:10.1021/nn4046634
Also from time-propagation!
◮ Talk by M. Kuisma
Tuomas Rossi / tuomas.rossi aalto.fi / GPAW 2016 / Jyväskylä 36/47
![Page 48: Nanoplasmonics within time-dependent density … · Outline Nanoplasmonics Methods and computations Analyzing the plasmonic response Case studies In this talk: Finite systems For](https://reader031.vdocuments.site/reader031/viewer/2022013117/5b082fdf7f8b9a3d018bce36/html5/thumbnails/48.jpg)
Outline
Nanoplasmonics
Methods and computations
Analyzing the plasmonic response
Case studies
Quantized evolution of the plasmonic response in a
stretched nanorod
. . .
Tuomas Rossi / tuomas.rossi aalto.fi / GPAW 2016 / Jyväskylä 37/47
![Page 49: Nanoplasmonics within time-dependent density … · Outline Nanoplasmonics Methods and computations Analyzing the plasmonic response Case studies In this talk: Finite systems For](https://reader031.vdocuments.site/reader031/viewer/2022013117/5b082fdf7f8b9a3d018bce36/html5/thumbnails/49.jpg)
Outline
Nanoplasmonics
Methods and computations
Analyzing the plasmonic response
Case studies
Quantized evolution of the plasmonic response in a
stretched nanorod
. . .
Tuomas Rossi / tuomas.rossi aalto.fi / GPAW 2016 / Jyväskylä 38/47
![Page 50: Nanoplasmonics within time-dependent density … · Outline Nanoplasmonics Methods and computations Analyzing the plasmonic response Case studies In this talk: Finite systems For](https://reader031.vdocuments.site/reader031/viewer/2022013117/5b082fdf7f8b9a3d018bce36/html5/thumbnails/50.jpg)
Stretched nanorod
The nanorod
◮ 261 sodium atoms
◮ length 5.0 nm
◮ diameter 1.3 nm
T. P. Rossi, A. Zugarramurdi, M. J. Puska, and R. M. Nieminen,Phys. Rev. Lett. 115, 236804 (2015). doi:10.1103/PhysRevLett.115.236804
Tuomas Rossi / tuomas.rossi aalto.fi / GPAW 2016 / Jyväskylä 39/47
![Page 51: Nanoplasmonics within time-dependent density … · Outline Nanoplasmonics Methods and computations Analyzing the plasmonic response Case studies In this talk: Finite systems For](https://reader031.vdocuments.site/reader031/viewer/2022013117/5b082fdf7f8b9a3d018bce36/html5/thumbnails/51.jpg)
Stretched nanorod
The nanorod
◮ 261 sodium atoms
◮ length 5.0 nm
◮ diameter 1.3 nm
Computational details
◮ DFT and TDDFT
◮ APBE xc functional
T. P. Rossi, A. Zugarramurdi, M. J. Puska, and R. M. Nieminen,Phys. Rev. Lett. 115, 236804 (2015). doi:10.1103/PhysRevLett.115.236804
Tuomas Rossi / tuomas.rossi aalto.fi / GPAW 2016 / Jyväskylä 39/47
![Page 52: Nanoplasmonics within time-dependent density … · Outline Nanoplasmonics Methods and computations Analyzing the plasmonic response Case studies In this talk: Finite systems For](https://reader031.vdocuments.site/reader031/viewer/2022013117/5b082fdf7f8b9a3d018bce36/html5/thumbnails/52.jpg)
Stretched nanorod
The nanorod
◮ 261 sodium atoms
◮ length 5.0 nm
◮ diameter 1.3 nm
Computational details
◮ DFT and TDDFT
◮ APBE xc functional
(animation)
T. P. Rossi, A. Zugarramurdi, M. J. Puska, and R. M. Nieminen,Phys. Rev. Lett. 115, 236804 (2015). doi:10.1103/PhysRevLett.115.236804
Tuomas Rossi / tuomas.rossi aalto.fi / GPAW 2016 / Jyväskylä 39/47
![Page 53: Nanoplasmonics within time-dependent density … · Outline Nanoplasmonics Methods and computations Analyzing the plasmonic response Case studies In this talk: Finite systems For](https://reader031.vdocuments.site/reader031/viewer/2022013117/5b082fdf7f8b9a3d018bce36/html5/thumbnails/53.jpg)
Stretched nanorod
The nanorod
◮ 261 sodium atoms
◮ length 5.0 nm
◮ diameter 1.3 nm
Computational details
◮ DFT and TDDFT
◮ APBE xc functional
T. P. Rossi, A. Zugarramurdi, M. J. Puska, and R. M. Nieminen,Phys. Rev. Lett. 115, 236804 (2015). doi:10.1103/PhysRevLett.115.236804
Tuomas Rossi / tuomas.rossi aalto.fi / GPAW 2016 / Jyväskylä 39/47
![Page 54: Nanoplasmonics within time-dependent density … · Outline Nanoplasmonics Methods and computations Analyzing the plasmonic response Case studies In this talk: Finite systems For](https://reader031.vdocuments.site/reader031/viewer/2022013117/5b082fdf7f8b9a3d018bce36/html5/thumbnails/54.jpg)
Stretched nanorod
The nanorod
◮ 261 sodium atoms
◮ length 5.0 nm
◮ diameter 1.3 nm
Computational details
◮ DFT and TDDFT
◮ APBE xc functional
A B C D E F G H
T. P. Rossi, A. Zugarramurdi, M. J. Puska, and R. M. Nieminen,Phys. Rev. Lett. 115, 236804 (2015). doi:10.1103/PhysRevLett.115.236804
Tuomas Rossi / tuomas.rossi aalto.fi / GPAW 2016 / Jyväskylä 39/47
![Page 55: Nanoplasmonics within time-dependent density … · Outline Nanoplasmonics Methods and computations Analyzing the plasmonic response Case studies In this talk: Finite systems For](https://reader031.vdocuments.site/reader031/viewer/2022013117/5b082fdf7f8b9a3d018bce36/html5/thumbnails/55.jpg)
Plasmonic response during stretching
Longitudinal excitation
T. P. Rossi, A. Zugarramurdi, M. J. Puska, and R. M. Nieminen,Phys. Rev. Lett. 115, 236804 (2015). doi:10.1103/PhysRevLett.115.236804
Tuomas Rossi / tuomas.rossi aalto.fi / GPAW 2016 / Jyväskylä 40/47
![Page 56: Nanoplasmonics within time-dependent density … · Outline Nanoplasmonics Methods and computations Analyzing the plasmonic response Case studies In this talk: Finite systems For](https://reader031.vdocuments.site/reader031/viewer/2022013117/5b082fdf7f8b9a3d018bce36/html5/thumbnails/56.jpg)
Plasmonic response during stretching
Longitudinal excitation
T. P. Rossi, A. Zugarramurdi, M. J. Puska, and R. M. Nieminen,Phys. Rev. Lett. 115, 236804 (2015). doi:10.1103/PhysRevLett.115.236804
Tuomas Rossi / tuomas.rossi aalto.fi / GPAW 2016 / Jyväskylä 40/47
![Page 57: Nanoplasmonics within time-dependent density … · Outline Nanoplasmonics Methods and computations Analyzing the plasmonic response Case studies In this talk: Finite systems For](https://reader031.vdocuments.site/reader031/viewer/2022013117/5b082fdf7f8b9a3d018bce36/html5/thumbnails/57.jpg)
Quantized evolution of the plasmonic response
A B C D E F G H
T. P. Rossi, A. Zugarramurdi, M. J. Puska, and R. M. Nieminen,Phys. Rev. Lett. 115, 236804 (2015). doi:10.1103/PhysRevLett.115.236804
Tuomas Rossi / tuomas.rossi aalto.fi / GPAW 2016 / Jyväskylä 41/47
![Page 58: Nanoplasmonics within time-dependent density … · Outline Nanoplasmonics Methods and computations Analyzing the plasmonic response Case studies In this talk: Finite systems For](https://reader031.vdocuments.site/reader031/viewer/2022013117/5b082fdf7f8b9a3d018bce36/html5/thumbnails/58.jpg)
Junction electronic structureF
1 (m = 0, n = 1)
2 (m = ±1, n = 1)
−3 −2 −1 0Energy (eV)
jDOS (arb.u.)
1
2
Junction projected DOS
T. P. Rossi, A. Zugarramurdi, M. J. Puska, and R. M. Nieminen,Phys. Rev. Lett. 115, 236804 (2015). doi:10.1103/PhysRevLett.115.236804
Tuomas Rossi / tuomas.rossi aalto.fi / GPAW 2016 / Jyväskylä 42/47
![Page 59: Nanoplasmonics within time-dependent density … · Outline Nanoplasmonics Methods and computations Analyzing the plasmonic response Case studies In this talk: Finite systems For](https://reader031.vdocuments.site/reader031/viewer/2022013117/5b082fdf7f8b9a3d018bce36/html5/thumbnails/59.jpg)
Junction electronic structure – Evolution
A B C D E F G H
0 10 20 30Elongation (Å)
−3
−2
−1
0
Ener
gy (e
V)
x2
A B C D E F G H
0
M
jDOS
Associated (m, n) states:1. (0, 1)2. (±1, 1)3. (±2, 1) and (0, 2)4. (±3, 1)5. (±1, 2)
T. P. Rossi, A. Zugarramurdi, M. J. Puska, and R. M. Nieminen,Phys. Rev. Lett. 115, 236804 (2015). doi:10.1103/PhysRevLett.115.236804
Tuomas Rossi / tuomas.rossi aalto.fi / GPAW 2016 / Jyväskylä 43/47
![Page 60: Nanoplasmonics within time-dependent density … · Outline Nanoplasmonics Methods and computations Analyzing the plasmonic response Case studies In this talk: Finite systems For](https://reader031.vdocuments.site/reader031/viewer/2022013117/5b082fdf7f8b9a3d018bce36/html5/thumbnails/60.jpg)
Electronic structure → Transport
0 10 20 30Elongation (Å)
−3
−2
−1
0
Ener
gy (e
V)
x2
A B C D E F G H
0
M
jDOS
0 10 20 30Elongation (Å)
0
2
4
6
8
10
Cond
ucta
nce
(G0
)
6
3
1
Conductance of the junctionA B C D E F G H
Associated (m, n) states:1. (0, 1)2. (±1, 1)3. (±2, 1) and (0, 2)4. (±3, 1)5. (±1, 2)
◮ Quantized 1DEG “bands”
serve as conduction
channels
T. P. Rossi, A. Zugarramurdi, M. J. Puska, and R. M. Nieminen,Phys. Rev. Lett. 115, 236804 (2015). doi:10.1103/PhysRevLett.115.236804
Tuomas Rossi / tuomas.rossi aalto.fi / GPAW 2016 / Jyväskylä 44/47
![Page 61: Nanoplasmonics within time-dependent density … · Outline Nanoplasmonics Methods and computations Analyzing the plasmonic response Case studies In this talk: Finite systems For](https://reader031.vdocuments.site/reader031/viewer/2022013117/5b082fdf7f8b9a3d018bce36/html5/thumbnails/61.jpg)
Origin of the quantized plasmonic evolution
0 10 20 30Elongation (Å)
0
2
4
6
8
10
Cond
ucta
nce
(G0
)
6
3
1
Conductance of the junctionA B C D E F G H
◮ Quantized transport reflected in coupled plasmon modes
(especially CTP)◮ Plasmonic counterpart of conductance quantization
T. P. Rossi, A. Zugarramurdi, M. J. Puska, and R. M. Nieminen,Phys. Rev. Lett. 115, 236804 (2015). doi:10.1103/PhysRevLett.115.236804
Tuomas Rossi / tuomas.rossi aalto.fi / GPAW 2016 / Jyväskylä 45/47
![Page 62: Nanoplasmonics within time-dependent density … · Outline Nanoplasmonics Methods and computations Analyzing the plasmonic response Case studies In this talk: Finite systems For](https://reader031.vdocuments.site/reader031/viewer/2022013117/5b082fdf7f8b9a3d018bce36/html5/thumbnails/62.jpg)
Outline
Nanoplasmonics
Methods and computations
Analyzing the plasmonic response
Case studies
Quantized evolution of the plasmonic response in a
stretched nanorod
. . .
Tuomas Rossi / tuomas.rossi aalto.fi / GPAW 2016 / Jyväskylä 46/47
![Page 63: Nanoplasmonics within time-dependent density … · Outline Nanoplasmonics Methods and computations Analyzing the plasmonic response Case studies In this talk: Finite systems For](https://reader031.vdocuments.site/reader031/viewer/2022013117/5b082fdf7f8b9a3d018bce36/html5/thumbnails/63.jpg)
Summary
Nanoplasmonics
Methods and computations
Time-dependent density-functional theory (TDDFT)
Time-propagation TDDFT with localized basis
Hybrid quantum–classical scheme
Practical aspects
Analyzing the plasmonic response
Spectra
Real-space quantities
Spatially resolved spectra
Electron transitions
Case studies
Quantized evolution of the plasmonic response in a
stretched nanorod
. . .
Tuomas Rossi / tuomas.rossi aalto.fi / GPAW 2016 / Jyväskylä 47/47