Nanoplasmonics within time-dependent density … · Outline Nanoplasmonics Methods and computations...
Transcript of Nanoplasmonics within time-dependent density … · Outline Nanoplasmonics Methods and computations...
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
Outline
Nanoplasmonics
Methods and computations
Analyzing the plasmonic response
Case studies
Tuomas Rossi / tuomas.rossi aalto.fi / GPAW 2016 / Jyväskylä 2/47
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
Outline
Nanoplasmonics
Methods and computations
Analyzing the plasmonic response
Case studies
Tuomas Rossi / tuomas.rossi aalto.fi / GPAW 2016 / Jyväskylä 3/47
Localized surface plasmonCollective oscillation of valence electrons
◮ Plenty of applications◮ Light confinement◮ Spectroscopy◮ Biomedicine◮ . . .
Plasmon resonance
◮ strong
◮ enhanced field
◮ tunable by◮ shape◮ composition◮ environment
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Plasmon coupling
Coupled plasmon modes (dipole-active):
Tuomas Rossi / tuomas.rossi aalto.fi / GPAW 2016 / Jyväskylä 5/47
Plasmon coupling
Coupled plasmon modes (dipole-active):
Tuomas Rossi / tuomas.rossi aalto.fi / GPAW 2016 / Jyväskylä 5/47
Nanoplasmonics
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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)
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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)
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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)
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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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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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)
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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
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
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
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
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
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
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
Induced density
Tuomas Rossi / tuomas.rossi aalto.fi / GPAW 2016 / Jyväskylä 30/47
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
Induced density → potential → electric near field
from gpaw.inducedfield.inducedfield_tddft import TDDFTInducedField
Tuomas Rossi / tuomas.rossi aalto.fi / GPAW 2016 / Jyväskylä 32/47
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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