Quantum plasmonics with adatoms on graphene flakes

Quantum plasmonics with adatoms

on graphene flakes

M. Müller, C. Rockstuhl

Karlsruhe Institute of Technology, Germany

M. Pelc, A. Ayuela

Donostia International Physics Center

M. Kosik, K. Słowik

Nicolaus Copernicus University in Toruń, Poland

Quantum plasmonics

Quantum emitters

placed near nanoantennas Emitter - light interactions

strong coupling

fast dynamics

absorption losses

limited tunability

Graphene plasmonics

extreme platform for plasmonics

tunability

extreme platform for plasmonics tunability

Koppens et al. Nano Letters (2011)

Graphene plasmonics

extreme platform for plasmonics tunability

ω _res ~ E _F ^1/2

Graphene plasmonics

extreme platform for plasmonics tunability

Graphene plasmonics

ω _res ~ ( E _F / L ) ^1/2

Renwen Yu et al. ACS Photonics (2017)

L

extreme platform for plasmonics tunability

Graphene plasmonics

Manjavacas et al. Nanophotonics (2013)

Graphene flakes

resonances in optical range

quantum model required for size < 20 nm

Thongrattanasiri et al. ACS Nano (2012)

Outline

Model

Applications

Graphene flake

arbitrary shape and edge type

small: <1000 C atoms (computation time, resonance in visible)

Adatom

one or more

Anderson model of one-, two- or few-level

defects

coupled to selected carbon sites

Laser beam

arbitrary temporal shape cw, Gaussian, δ(t), ...

classical, no feedback from atoms

Ingredients

Hamiltonian: flake

t

t t t

t t

t t

t t

t t

t t

0 1 2 3 4 5 6

0 1 2 3 4 5 6

t = - 2.66 eV

site basis

Hamiltonian: flake + atom

t

t t t

t t

t t

t t

t t

t t

ω_e ω_g

0 1 2 3 4 5 6 e g

0 1 2 3 4 5 6 e g

t = - 2.66 eV

site basis

Hamiltonian: flake + atom

t

t t t

t t

t t

t t

t t

t t

ω_e ω_g

0 1 2 3 4 5 6 e g

0 1 2 3 4 5 6 e g

t = - 2.66 eV

site basis

Atom energies evaluated with respect to Dirac point

of graphene

Hamiltonian: flake + atom

t

t t t

t t

t t

t t

t t

t t t_e t_g

t_e ω_e

t_g ω_g

0 1 2 3 4 5 6 e g

0 1 2 3 4 5 6 e g

t = - 2.66 eV

site basis

Ihnatsenka & Kirczenow, PRB (2011)

adatom Ψ ω_k t_k Δt₀

all quantities in units of t

Real - system parameters

H F OH

O

t

t t t

t t

t t

t t

t t

t t t_e t_g

t_e ω_e

t_g ω_g

Eigenstate basis

H Ψ _j = E _j Ψ _j

Ψ _j = Σ _l c _jl φ _l

E₁ E₂

E₃ E₄

E₅ E₆

E₇ E₈

E₉

Eigenstate basis

H Ψ _j = E _j Ψ _j

Ψ _j = Σ _l c _jl φ _l

Energy landscape

Field

Flake + adatom

tight - binding Hamiltonian

H(t) = H flake+adatom

+ H adatom+field

+ Φ _ext

+ Φ _ind

Field

H(t) = H flake+adatom

+ H adatom+field

+ Φ _ext

+ Φ _ind

Adatom + field

g

g

Field

H(t) = H flake+adatom

+ H adatom+field

+ Φ _ext

+ Φ _ind

Adatom + field

g

g

Field

H(t) = H flake+adatom

+ H adatom+field

+ Φ _ext

+ Φ _ind

External potential

coupling of flake and field (Φ

)

= - e r

· E(t)

r

- position of site k E(t) - laser field

diagonal in site basis

Cox et al. Nature Communications (2014)

Field

H(t) = H flake+adatom

+ H adatom+field

+ Φ _ext

+ Φ _ind

Induced potential

Coulomb interaction + exchange integrals on flake

on atom if ≠ 1 electron

inbetween scaled with t

, t

Potasz et al. PRB (2012)

Field

H(t) = H flake+adatom

+ H adatom+field

+ Φ _ext

+ Φ _ind

Induced potential

Coulomb interaction + exchange integrals on flake

on atom if ≠ 1 electron

inbetween scaled with t

, t

doping with electrons or holes

Equilibrium state

eigenbasis

site basis

no doping 1 doping

electron

2 doping electrons

5 doping electrons

Equilibrium state

eigenbasis

site basis

2/N

0

Eigenstate charge distributions

-7.52 eV lowest

-4.30 eV edge

-1.11 eV HOMO

1.11 eV LUMO

1.64 eV

Eigenstates with adatom

HOMO LUMO

t_e,g = 0.5 eV

Eigenstates with adatom

t_e,g = 1.0 eV

HOMO LUMO

Density matrix dynamics

master equation

Density matrix dynamics

master equation

decoherence

via Lindblad terms

Density matrix dynamics

master equation

decoherence

via Lindblad terms

decoherence between selected pair of states

Density matrix dynamics

master equation

decoherence

via Lindblad terms

phenomenologically

decoherence between selected pair of states

-

Induced charge

Illumination

@ HOMO-LUMO transition

time

Induced charge

Illumination

@ HOMO-LUMO transition

time

Illumination

< HOMO-LUMO transition,

doped flake

see Manjavacas et al. Nanophotonics (2013)

Induced charge

Induced charge

DFT simulations by Giulia Giannone (Istituto Italiano di Tecnologia, Lecce)

Comparison of

induced charge

distribution plots

obtained from DFT

and our code.

Charge dynamics with atom

0.000025

0 t ~ 1 fs

t ~ 20 fs

Coupling flakes to adatoms

time (fs)

Ω = E d _HL

Coupling flakes to adatoms

time (fs)

Coupling flakes to adatoms

time (fs)

Coupling flakes to adatoms

time (fs)

Rabi regime

Poster advertisement

Interaction of a graphene nanoflake with an adatom under optical illumination M. Kosik et al., poster

transition dipole moment of adatom, flake & combined

Rabi oscillations in flake + adatom

spontaneous emission characteristics

Miriam

Decoherence dynamics

via Lindblad terms phenomenologically

known for pristine graphene 1 parameter τ

decay to predefined stationary state

not known, but scalable 2+ free parameters γ

not protected against Pauli principle breaking

= ?

-

Decoherence dynamics

time

“HOMO”

“LUMO”

Decoherence dynamics

time

“HOMO”

“LUMO”

Decoherence dynamics

time

corrected

“HOMO”

“LUMO”

Polarizability

time (fs)

x

y

Absorption spectrum

Blue shifting resonances

➔ require doping

➔ lower energy

Red shifting resonances

➔ do not require doping

➔ higher energy

➔ motion of electron cloud

➔ collective process

➔ ± doping required

➔ shift with doping ~n^1/2

➔ nonlinear optical response

➔ “intraband” → lower energy

➔ creation of an electron-hole pair

➔ single-particle process

➔ appear without doping

➔ might disappear with doping

➔ “Interband” → higher energy

Excitons or plasmons

➔ motion of electron cloud

➔ collective process

➔ ± doping required

➔ shift with doping ~n^1/2

➔ nonlinear optical response

➔ “intraband” → lower energy

➔ creation of an electron-hole pair

➔ single-particle process

➔ appear without doping

➔ might disappear with doping

➔ “Interband” → higher energy

Excitons or plasmons

Bernadotte et al. J. Phys. Chem. C (2013) Townsend& Bryant J.Opt. (2014)

G. Bryant J. Opt. (2016)

Zhang et al. ACS nano (2017)

….

Poster advertisement

Co-Existence of Tunable Plasmons and Excitons in Graphene Nanoantennas M. Müller et al., poster

mostly excitonic transition predominantly plasmonic transition

➔ Tool to study dynamics of illuminated graphene flakes with adatoms

◆ Spectral properties (eigenenergies and states)

◆ Dynamics of density matrix

◆ Induced charges & optical response

➔ Distinction of plasmonic & excitonic resonances

➔ Influence of flake on adatom’s optical response & vice-versa

Summary & outlook

➔ Tool to study dynamics of illuminated graphene flakes with adatoms

◆ Spectral properties (eigenenergies and states)

◆ Dynamics of density matrix

◆ Induced charges & optical response

➔ Distinction of plasmonic & excitonic resonances

➔ Influence of flake on adatom’s optical response & vice-versa

➔ more atoms

➔ back-action on field

Summary & outlook

➔ Tool to study dynamics of illuminated graphene flakes with adatoms

◆ Spectral properties (eigenenergies and states)

◆ Dynamics of density matrix

◆ Induced charges & optical response

➔ Distinction of plasmonic & excitonic resonances

➔ Influence of flake on adatom’s optical response & vice-versa

➔ more atoms

➔ back-action on field

Summary & outlook

thank you