Biomedical Engineering Reference
In-Depth Information
Fig. 10.4
A QDM coupled by electron tunneling. (
a
) At zero bias the laser field pumps a spatially
direct exciton, where both hole and electron are localized in the same QD; this corresponds to
a plateau on the
F
-dependent eigenvalue spectrum. (
b
) The field tilts the band edges, inducing
a resonance among the conduction bands of the two QDs; electron tunneling occurs, mixing the
direct with the spatially indirect exciton with an anticrossing opening in the spectrum
exciton states are superpositions of a spatially direct and indirect states and are
therefore truly molecular in nature [
3
,
4
].
The effect of the external axial electric field is to induce, on the one hand,
a quantum confined Stark effect (QCSE) shift of the exciton levels within each
individual QD. On the other hand, it exerts a DC Stark shift of excitons with spatially
indirect character, effectively separating electron and holes in opposite directions. In
what follows we ignore QCSE since it will be rather small for the set of parameters
used in our simulations. The Stark shift on spatially indirect exciton shifts the energy
by
eFd
. With this in mind, we can finally write the interacting effective QDM
excitonic Hamiltonian as
Δ
S
=
⎛
⎝
⎞
⎠
δ
0
Ω
T
0
0
Ω
B
01
01
Ω
T
δ
t
e
t
h
V
F
H
10
=
0
t
e
δ
01
+
Δ
S
0
t
h
,
(10.13)
01
0
t
h
0
δ
10
−
Δ
S
t
e
10
10
Ω
B
V
F
t
h
t
e
δ
01
10
01
10
where the columns are associated with the states
|
0
,
|
01
X
,
|
01
X
,
|
10
X
,and
|
10
X
,
where the third and fourth columns represent spatially indirect excitons.
