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a
|2>
even-parity state
E
2
Δ
E
<0|x |1>
|1>
odd-parity state
E
1
<1|x |2>
|0>
ground state
0
b
c
Ni-Br-Br
25
PDBS
PDTDS
1.0
Ni-Cl-Cl
PDHS
PPV
20
0.8
MEH-PPV
Pt-Cl
Ni-Cl-NO
3
PDA
0.6
Pt-Br
15
0.4
Sr
2
CuO
3
Pt-I
0.2
Pt-I
10
Ni-Cl-NO
3
Ca
2
CuO
3
0.0
Pt-Br
Ni-Cl-Cl
Ni-Br-Br
Pt-Cl
-0.2
Sr
2
CuO
3
5
PDA
Ca
2
CuO
3
PDHS
-0.4
1.0
2.0
3.0
4.0
Optical gap energy (eV)
0
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
<0|x |1> (Å)
Fig. 7.6 (a) Three-level structure consisting of ground state, odd-parity state, and even-parity
state. (b) The energy difference between the odd-parity state and even-parity state is plotted versus
the optical gap energy. (c) The transition dipole moments between the two excited states |1
>
and
|2
are plotted versus the transition dipole moment between the ground state and odd-parity state.
From [
10
]
>
e ¼ e
1
þ
i
e
2
¼ e
0
½
1
þ w
ð
1
Þ
are taken into account. Moreover, considering the relation,
w
ð
3
Þ
E
2
e
0
w
ð
3
Þ
E
2
þ
3
,
De
2
spectrum is obtained from the relation,
De
2
¼
Im
½
3
. Here,
E
is
the applied electric field.
The
De
2
curve for Ni-Br-Br calculated by the three-level model is shown in
Fig.
7.4b
by the broken line, which reproduces well the oscillating behavior of the
experimental
De
2
spectrum. From this analysis, two important features are obtained;
one is that the energy difference (
DE ¼ ho
2
ho
1
) of the two excited states is very
small, being 10 meV. The other is that the transition dipole moments between |1
>
and |2
>
(
<
1
jxj
2
>
) is very large, exceeding 20
˚
. The analysis indicates the
existence of two discrete levels of excited states. It is, therefore, reasonable to
consider that both |1
>
and |2
>
are not due to the continuum but due to excitonic
states.
Similar analyses of the ER spectra in the other Ni-X chain compounds revealed
that those two features in the
w
ð
3
Þ
ðo;
De
2
or
0
;
0
; oÞ
spectra are common in Ni-X
chain compounds. In Fig.
7.6b
, the energy difference
DE
of the two excited states is
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