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Sabas Abuabara, Luis G.C. Rego and Victor S. Batista
Department of Chemistry, Yale University, New Haven, CT 06520-8107
Creating and Manipulating Electronic Coherences in Functionalized
Semiconductor Nanostructures
35th Winter Colloquium on The Physics of Quantum ElectronicsSnowbird, Utah -- January 2-6, 2005
TiO2-anatase semiconductor nanostructure functionalized with catechol adsorbates
Aspects of Study• Interfacial Electron Transfer Dynamics
– Relevant timescales and mechanisms– Dependence of electronic dynamics on the
crystal symmetry and dynamics• Effect of nuclear dynamics
– Whether nuclear motion affects transfer mechanism or timescale
– Implications for quantum coherences • Hole Relaxation Dynamics
– Decoherence timescale– Possibility of coherent control
L.G.C. Rego, S.T. Abuabara and V.S. Batista, J. Chem. Phys., submitted (2004)
L.G.C. Rego, S.T. Abuabara and V.S. Batista Quant. Inform. Comput., submitted (2004)
S. Flores and V.S. Batista J. Phys. Chem. B 108 ,6745 (2004)
L.G.C. Rego and V.S. Batista, J. Am. Chem. Soc. 125, 7989 (2003)
V.S. Batista and P. Brumer, Phys. Rev. Lett. 89, 5889 (2003), ibid. 89, 28089 (2003)
Model System – Unit Cell
TiO2-anatase nanostructure functionalized by adsorbed catechol
124 atoms:
32 [TiO2] units = 96catechol [C6H6-202] unit = 1216 capping H atoms = 16
VASP/VAMP simulation packageHartree and Exchange Correlation Interactions: Perdew-Wang
functional Ion-Ion interactions: ultrasoft Vanderbilt pseudopotentials
Phonon Spectral Density
O-H stretch, 3700 cm-1
(H capping atoms)
C-H stretch
3100 cm-1
TiO2 normal modes
262-876 cm-1
C-C,C=C stretch
1000 cm-1,1200 cm-1
[010]
Accurate description of charge delocalization requires simulations in extended model systems.
•Simulations in small clusters (e.g., 1.2 nm nanostructures) are affected by surface states that speed up the electron injection process
• Periodic boundary conditions alone often introduce artificial recurrencies (back-electron transfer events).
Simulations of Electronic Relaxation
Three unit cells extending the system in [-101] direction
[-101]
Electronic HamiltonianH is the Extended Huckel Hamiltonian in the basis of Slater type atomic orbitals (AO’s) including• 4s, 3p and 3d AO’s of Ti 4+ ions• 2s and 2p AO’s of O 2- ions• 2s and 2p AO’s of C atoms• 1s AO’s of H atoms • 596 basis functions per unit cell
S is the overlap matrix in the AO’s basis set.
..
How good is this tight binding Hamiltonian?
HOMO
LUMO,LUMO+1
Valence Band Conduction BandBand gap =3.7 eV
ZINDO1 Band gap =3.7 eV
Exp. (2.4 nm) = 3.4 eV
Exp. (Bulk-anatase) = 3.2 eV
Electronic Density of States (1.2 nm particles)
HOMO
photoexcitation
Mixed Quantum-Classical Dynamics Propagation Scheme
)0()(ˆ)( tUt
and withq
qq ttBt )()()(
')'(
)(ˆ dttHi
etU , where
i
iqiq tKtCt )()()( , are the instantaneous MO’s
)()()()()( tEtCtStCtH
obtained by solving the extended-Hückel generalized eigenvalue equation:
)()()()( 2))()((
tptqetBtBp
tEtEi
pq
qp
2))()((
)()(
tEtE
i
qp
etBtB
Which in 0 limit we approximate as
Propagation Scheme
Propagation Scheme cont’d
Derive propagator for midpoint scheme:Hamiltonian changes linearly during time step /
Forward and Backwards propagation equal
)()()()(ˆ 2)(
2 tqetBttUq
tEi
q
q
)()(
)(),(ˆ
2)(
2
tqetB
tttU
tEi
q
Injection from LUMO
TiO2 system extended in [-101] direction with PBC in [010] direction
Grey ‘Balloons’ are isosurface of electronic
density
Allow visualization of
mechanism
With this scheme, we can calculate for all t>0 :• electronic wavefunction• electronic density • Define the Survival Probability for electron(hole) to be found on specific adsorbate molecule
SYS
j
jij
MOL
iiMOL StCtCtP
,
,,,
,
*, )()()(
Propagation Scheme cont’d
LUMO InjectionP
MO
L(t)
Relaxation Dynamics of Hole States Localized on Adsorbate Monolayer
t=15 ps Super-exchange hole transfer
SYS
j
jij
MOL
iiMOL StCtCtP
,
,,,
,
*, )()()(
Compute Hole Population on each adsorbateAfter photoinduced electron-
hole pair separation due toelectron injection
Hole is left behind, off resonant w.r.t.
conduction and valence bands
Dynamics on Adsorbate Monolayer
0 20 40 60 80 1000.0
0.2
0.4
0.6
0.8
1.0
SU
RV
IVA
L P
RO
BA
BIL
ITY
TIME (PS)
Coherent Hole-Tunneling Dynamics
);(/
)(22
2
22
sin ttPjk
jk
jkj
22 )2/()/( jkjkjk
PM
OL(
t)P
MO
L(t)
(1)
(2)
(3)
Measure of Decoherence and Localization
Survival of Electronic Coherences
Inhibiting Hole Super-Exchange by multiple 2 pulses
CB
VB
C
L
superexchange
Adsorbate molecules (C, L,…)TiO2 semiconductor
We investigate the feasibility of manipulating the underlying hole relaxation dynamics by merely affecting the relative phases of the state components (e.g., by using femtosecond laser pulses)
HOMO-1
LUMO
HOMO2 pulses
hole
Inhibiting Hole Super-Exchange by multiple 2 pulses, cont’d
Proposals for the Inhibition of Decay by Using Pulses:
• G.S. Agarwal, M.O. Scully and H. Walther (a) Phys. Rev. Lett. 86, 4271 (2001); (b) Phys. Rev. A 63, 44101 (2001)
• L. Viola and S. Lloyd Phys. Rev. A 58, 2733 (1998),• L. Viola, E. Knill and S. Lloyd Phys. Rev. Lett. 82, 2417 (1999)
• D. Vitali and P. Tombesi Phys. Rev. A 59, 4178 (1999)
• W.M. Itano, D.J. Heinzen, J.J. Bollinger and D.J. Wineland Phys. Rev. A 41, 2295 (1990)
)0()0()0(
)()0(2)()(
t
ttt= k*
= 200 fs,
Inhibiting Hole Super-Exchange by multiple 2 pulses, cont’d
2- pulses (200 fs spacing)
Apply pulsed radiation tuned to frequency 21
Investigation of Coherent-Control cont’d
0 20 40 60 80 1000.0
0.2
0.4
0.6
0.8
1.0
S
UR
VIV
AL
PR
OB
AB
ILIT
Y
TIME (PS)
2- pulses (200 fs spacing)
14 fs 60 fs
0 20 40 60 80 1000.0
0.2
0.4
0.6
0.8
1.0
S
UR
VIV
AL
PR
OB
AB
ILIT
Y
TIME (PS)
2- pulses (200 fs spacing)
2 fs 42 fs
Investigation of Coherent-Control cont’d
•We have investigated interfacial electron transfer and hole tunneling relaxation dynamics according to a mixed quantum-classical approach that combines ab-initio DFT molecular dynamics simulations of nuclear motion with coherent quantum dynamics simulations of electronic relaxation.
•We have investigated the feasibility of creating entangled hole-states localized deep in the semiconductor band gap. These states are generated by electron-hole pair separation after photo-excitation of molecular surface complexes under cryogenic and vacuum conditions.
•We have shown that it should be possible to coherently control superexchange hole-tunneling dynamics under cryogenic and vacuum conditions simply by applying a sequence of ultrashort 2-pulses with a frequency that is resonant to an auxiliary transition in the initially populated adsorbate molecule.
•We conclude that large scale simulations of quantum dynamics in complex molecular systems can provide valuable insight into the behavior of the quantum coherences in exisiting materials which might be essential to bridge the gap between the quantum information and quantum control communities.
Conclusions
•NSF Nanoscale Exploratory Research (NER) Award ECS#0404191•NSF Career Award CHE#0345984•ACS PRF#37789-G6•Research Corporation, Innovation Award•Hellman Family Fellowship•Anderson Fellowship•Yale University, Start-Up Package•NERSC Allocation of Supercomputer Time •PQE XXXV Organizers: M. Scully, G. R. Welch, M. S. Zubairy, P. Brumer
Thank you !
Acknowledgment