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insulator, the intramolecular excitation indicated by the open arrow (the upper
figure of Fig.
7.7a
) corresponds to the lowest excited state |1
with odd-parity.
The in-phase combination of the intermolecular CT excited states indicated by the
broken arrows corresponds to the second lowest excited state |2
>
>
with even-parity.
>
Excited electron and hole occupies the same site in |1
, but the different sites in
>
>
|2
forms an exciton with large binding energy due to the large
electron-hole Coulomb attractive interaction and therefore
. State |1
DE
is considerably
enhanced. The envelopes of the exciton wave functions are shown in the lower
part of Fig.
7.7a
. A large difference in the spatial extensions of |1
>
and |2
>
is
unfavorable for obtaining a large dipole moment
<
1
jxj
2
>
.
As for the electronic structure and excited states of 1D Mott insulators, we
consider a single band Hubbard model shown in Fig.
7.7b
. It is known that
fundamental electronic properties of CT insulators can be discussed using such a
simplified model. In this model, the electron vacancy (holon) and double electron
occupancy (doublon) are prohibited to stay on the same site. As a result, the odd
excited state |1
correspond, respectively, to the out-
of phase and in-phase combination of the two CT states |R
>
and the even excited state |2
>
indicated by
open arrows in the upper part of Fig.
7.7b
. When
U
is much larger than the transfer
energy
t
, splitting
>
and |L
>
should be small and their wave
functions should be similar to each other except for their phases as illustrated in
the lower part of Fig.
7.7b
. In this case, a spatial overlap of the wave functions
between |1
DE
between |1
>
and |2
>
>
and |2
>
becomes very large, leading to a large
<
1
jxj
2
>
[
16
]. This is
w
ð
3
Þ
ðo;
the enhancement mechanism of
0
;
0
; oÞ
in 1D Mott insulators.
7.3.2 Third-Harmonic Generation Spectroscopy
jw
ð
3
Þ
ð
o; o; o; oÞj
The
spectrum obtained from the reflection-type THG
measurements on a Ni-Br-Br single crystal is shown in Fig.
7.8b
[
11
]. The
spectrum exhibits a strong enhancement (labeled as A in the figure) when the
photon energy of the incident light is 0.43 eV. This energy corresponds to the 1/3
of the CT transition energy of Ni-Br-Br. Therefore, the enhancement is attributed
to the three-photon resonance to state |1
3
>
.
jw
ð
3
Þ
ð
spectrum has other two resonant structures, B and C,
which are located at around 0.65 eV and 0.5 eV, respectively. The twice energy of
structure B (~1.3 eV) is close to the CT transition energy (1.27 eV), which is
determined from the
The
3
o; o; o; oÞj
e
2
spectrum. Since the ER spectroscopy revealed that even-
parity CT state |2
as mentioned above,
structure B could be assigned to the two-photon resonance to state |2
>
is close in energy to odd-party CT state |1
>
>
.
e
2
spectrum at 4 K shown in the inset of
Fig.
7.8c
gives valuable information [
11
]. The
As for the assignment of structure C, the
e
2
spectrum has a weak shoulder
structure at around 1.5 eV, which is equal to the triplicate energy of structure C
(0.5 eV) in Fig.
7.8b
. This suggests that structure C would be related to the
three-photon resonance to another odd-parity state |3
>
located at the higher energy
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