Chemistry Reference
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Fig. 7.5 max
j
Im
w
ð
3
Þ
ðo;
0
;
0
; oÞj
values for Ni-X
and other 1D materials are
plotted versus the optical
gap energies.
PA
polyacetylene,
PDA
polydiacetylene,
PTV
poly
(thienylene-vinylene),
PPV
poly(
p
-phenylene-vinylene),
PDHS
poly(di-hexylsilane).
From [
10
]
10
-4
Ni-Br-Br
Ni-Cl-Cl
10
-6
Ni-Cl-NO
3
Sr
2
CuO
3
Ca
2
CuO
3
10
-8
Pt-I
PDA
PA
PTV
Pt-Br
PPV
10
-10
Pt-Cl
PDHS
1
2
3
4
Optical gap energy (eV)
other 1D semiconductors; 1D cuprates of Sr
2
CuO
3
and Ca
2
CuO
3
, Pt-X chain
compounds (X
¼
Cl, Br, and I),
p
-conjugated polymers (PA, PDA, PTV, and
PPV), and
-conjugated polymers (PDHS). 1D cuprates have the same electronic
structure (1D Mott insulator states) as Ni-X chain compounds and show similar
linear and nonlinear optical properties. In Fig.
7.5
, therefore, data points of both
Ni-X chain compounds and 1D cuprates were shown by the same solid circles.
Pt-X chain compounds (Pt-Cl, Pt-Br, and Pt-I in Fig.
7.5
) and
s
-conjugated
polymers (PA, PDA, PTV, and PPV in Fig.
7.5
) belong to Peierls insulators, and
a
p
w
ð
3
Þ
j
values
of Pt-X chain compounds and conjugated polymers are roughly scaled by the
optical gap energies
E
g
as max
s
-conjugated polymer (PDHS in Fig.
7.5
) to band insulators. max
j
Im
w
ð
3
Þ
j
values of Ni-X chain compounds (Ni-Br-Br, Ni-Cl-Cl, and Ni-Cl-NO
3
) show a
significant enhancement as compared to those in 1D Peierls and band insulators.
In order to unravel the origin for the enhancement of
w
ð
3
Þ
j/E
g
6
. On the other hand, max
j
Im
j
Im
(3)
in Ni-X chain
compounds, the three-level model shown in Fig.
7.6a
was adopted. In 1D electronic
systems, it is known that the third-order optical nonlinearity is governed by three or
four states, which are so-called essential states [
15
]. The three-level model consists
of three states; ground state |0
w
>
, an odd-parity state |1
>
, and an even-parity state
|2
is a one-photon-allowed state and observed by a linear
optical measurement such as absorption and reflectance spectroscopy. The even-
parity state |2
>
. The odd-parity state |1
>
>
is a one-photon-forbidden state. Within the three-level model, the
dominant term of
w
ð
3
Þ
ðo;
0
;
0
; oÞ
is expressed as follows:
Ne
4
3
2
2
<
2
jxj
1
>
<
1
jxj
0
>
w
ð
3
Þ
ðo;
0
;
0
; oÞ¼
(7.3)
e
0
h
3
2
ðo
1
o ig
1
Þ
ðo
2
o ig
2
Þ
Here,
N
is the density of the relevant electrons,
e
is the charge of electron,
e
0
is
the dielectric constant of vacuum,
x
is the displacement along the 1D axis,
ho
1
ðho
2
Þ
is
the energy position of the state |1
>
(|2
>
)and
g
1
ðg
2
Þ
is the damping energy of the state
|1
>
(|2
>
). In the fitting calculation, all the 12 terms including the dominant term (
7.3
)
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