Exciton diffusion, splitting excitons and exciton-plasmon interactions

George C. SchatzNorthwestern University

Quantum Days, Bilbao, July13, 2015

Exciton Dynamics

Craig Chapman Sameer Patwardhan Montacer Dridi

Joe Hupp Teri Odom Emily Weiss

Outline1)Förster Transfer (FRET) and its application to

MOFs

2)Quantum Cutting and Space Separated ExcitonFission

3) Plasmon-Exciton Interactions and Lasers

Förster Energy Transfer

22ET DAk J OI

3

3 D A D A

DA

r rJ higher order corr

r

D AOI F E A E dE

Exciton Coupling: JDA

Overlap Integral OI:

2 22

6 6D A D A

DAf fJ

r r

6D A DA

ETf f OIk

r

Excitontransfer rate:

More rigorous calculation (avoid dipole approx)

,

molNexciton r

m r mm r

C

† r s† r r† sm m l m m l

1 , 1 ,

1ˆ ˆ ˆ ˆ ˆ ˆ ˆH B B B B +B B2

mol molN N

r r rsm ml

m r m l r sm l

J

, ,

0 0

12 12 0

1 1 1| | | |4

m l t r t sN Ni jrs r s r s

ml m l m m l l m li j i j

q qJ

r r R R

is the position of atom i on molecule mRim

Exciton hamiltonian, in which the wavefunctionis a sum over molecules m, and over states r of each molecule.

J is the coupling between state r on molecule m, and state s on molecule l.

,t riq is the atomic transition density. This is e times the product of

ground and excited MO’s (for state r) projected onto atom i such that the sum over atoms gives the transition moment for the ground→r transition

Frenkel (1931), Longuet-Higgins, F. Spano and S. Matsika (Temple)

Metal Organic Frameworks (MOFs)

• Constituents: metal nodes, rigid organic ligands• Synthesis: solvothermal, post-synthesis

modifications• Properties: crystalline, highly porous• Applications: gas storage, catalysis

Porphyrin-based MOFs: F-MOF & DA-MOF

A B

D C

E

A

D

B

C

E

Zn

DA-ZnF

F-ZnP

F-MOF

DA-MOF

500 μm

500 μm

TCPB linker

Ho-Jin Son, Shengye Jin, Sameer Patwardhan, Sander J. Wezenberg, Nak Cheon Jeong, Monica So, Christopher E. Wilmer, Amy A. Sarjeant, George C. Schatz, Randall Q. Snurr, Omar K. Farha, Gary P. Wiederrecht, Joseph T. Hupp, J. Am. Chem. Soc., 135, 862-9 (2013).

DA-MOF has much larger OI than F-MOF

50% PL quenching with• F-MOF: 20% quencher• DA-MOF: 0.5% quencher !!

Quencher: FcPy

ZnPe-

Exciton diffusion on 20~30 ps timescale

Excitation: 446 nm

---ZnP---ZnP*---[ZnP---ZnP]n---ZnP*---ZnP---

kq FcPy

ke

Fluorescence Quenching Study

Hopping times: 1.4 ps for DA-MOF (2025 hops)620 ps for F-MOF (8 hops)

Förster Application

Direction Net Displacement (nm)

F-MOF DA-MOF

AB 2 nm 38 nm

AD 3 nm 29 nm

AE 1 nm 58 nmA

D

B

C

E

22ETk J OI

Expt 3 nm 53 nm

Convert rate to distance by factoring in fluorescence lifetime and lattice spacing, assuming incoherent scattering

Ho-Jin Son, Shengye Jin, Sameer Patwardhan, Sander J. Wezenberg, Nak Cheon Jeong, Monica So, Christopher E. Wilmer, Amy A. Sarjeant, George C. Schatz, Randall Q. Snurr, Omar K. Farha, Gary P. Wiederrecht, Joseph T. Hupp, J. Am. Chem. Soc., 135, 862-9 (2013).

Fission and pooling of excitons

Singlet Fission (SF)

POOLING

Known Up- and Down-conversion PhenomenaQuantum Cutting and Energy Pooling (rare-earths)

400% quantum cutting efficiency within ErxY2−xSi2O7 films using Er3+ as both sensitizer and activator

Miritello, et al., PRB, 81 (2010)

Space-Separated Quantum Cutting (Fission)

Timmerman, D.; Izeddin, I.; Stallinga, P.; Yassievich, I. N.; Gregorkiewicz, T. Space-separated quantumcutting with silicon nanocrystals for photovoltaic applications Nat. Photonics 2008, 2, 105-109.

E-field

e- cloud

Metalsphere

Plasmon excitation: collective excitation of the conduction electrons

osp 2

e

1shape / surroundings 2 cchemical properties 4 ne

m

Plasmon wavelength:

n=electron densityχ = shape factor (2 for sphere, >2 for spheroid)εo = dielectric constant of surroundings

Charge cloud of conduction electrons

Nuclear framework of particle

Mie Extinction for 13 nm Au spheres

0.0

0.2

0.4

0.6

0.8

1.0

Extin

ctio

n Ef

ficie

ncy

200 300 400 500 600 700 800

wavelength(nm)

300 400 500 600 700 800 9000

3

6

9

D/2r=521.51.251.01singleE

xtin

ctio

n E

ffici

ency

Wavelength (nm)

a

Extinction Spectra of Nanoparticle Chains

parallel

E0

Coupled multipole results for 100 30 nm spheres, parallel polarization

Parallel polarization leads to red shifts

320 340 360 380 400 4200

3

6

9

12

c perpendicular

E0

Perpendicular polarization leads to blue shifts

5.02.01.51.251.01single

E0

400 50 nm particles

Width=4 meV

Width=0.001meV

Shengli Zou, Nicolas Janel, and George C. Schatz, J. Chem. Phys.

120, 10871-10875 (2004).

Infinite array of 50 nm particles

Narrow lineshapes for one-dimensional arrays of silver particles spaced by the wavelength

Particle arrays made using optical lithography show sharp lattice plasmon resonances

W. Zhou and T. Odom, Nature Nano, 6, 423 (2011), W. Wang, G. C. Schatz and T. Odom, in preparation

Plasmon/exciton interactions lead to enhanced luminescence

Gilles R. Bourret, Tuncay Ozel, Martin Blaber, Chad M. Shade, George C. Schatz, Chad A. Mirkin, Nano Lett 13, 2270 (2013)

Extinction of hybridAbs/Pl of dye

Pl of hybrid Theory: Pl of hybrid

Nature Nano 8, 506-511 (2013)

Coupling QM to EM at the rate constant level

1)Quantum treatment of dye molecules

2)Classical electrodynamics for nanoparticle array

Model components:

Nature Nano 8, 506-511 (2013)

Measured and calculated dispersion behavior

Measured and calculated extinction

Coupling QM to EM at the rate constant level

3) Coupling of molecular polarization to field

22

2

( ) ( ) ( ) ( ) ( )a aa a a a

d P t dP t P t N t E tdt dt

2)Rate equations (derivable from Bloch equations) determine state populations, including amplified spontaneous and stimulated emission

1) Maxwell’s equations determine fields

Nature Nano 8, 506-511 (2013)

3 3 3

32 30

1 a

a

dN N N dPEdt dt

32 2

32 21

1 e

e

N dPdN N Edt dt

1 2 1

21 10

1 e

e

dPdN N N Edt dt

0 31

10 30

1 a

a

dN N dPN Edt dt

(S5)

Coupling QM to EM at the rate constant level

Results:(1) Emission shows threshold behavior

(2)Population inversion distribution show plasmon enhancement

Nature Nano 8, 506-511 (2013)

(3)Population inversion is pinned above the lasing threshold <50 nm from particles

Summary

1. Förster application with transition charges provides good qualitative modeling of MOFs. Proper description needs to handle multiple hops and coherence.

2. SSSF appears to be of comparable important to conventional singlet fission for organic dyes. Need to extend to quantum dot/dye structures.

3. Arrays of nanoparticles combined with laser dyes lead to hybrid excitonic/photonic/plasmonicresonances with narrow lines that are of interest in subwavelength lasers.