Chemistry Reference
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Fig. 8.26 (a) Level scheme
and the parameters of the
dp
model. (b) Obtained
optical conductivity spectra
for X
¼
Cl. (c) Same as (b),
but for X
¼
Br. Reprinted
from Matsuzaki et al. [
9
].
Copyright (2004) by the
American Physical Society
Fig.
8.25b
for PdBr as a Mott insulator. According to this expectation, the
measurements of optical conductivity spectra over the values of
x
from 0 to 1
were interpreted in the following way. Namely, the peak energy, which stays at
approximately 1.2 eV for
x ¼
0 ~ 0.3, makes a quick downward shift from
x ¼
0.3
to 0.4, and stays at 0.7 eV for
x ¼
0.4 ~ 0.8 [
9
]. Since, from the data of spin
susceptibility, we already know that the compound is more or less in the Mott-
insulator ground state, it was interpreted that these two Mott-insulator regions
correspond to the CT insulator of Ni (
x ¼
0 ~ 0.3) and the Mott-Hubbard insulator
of Pd (
x ¼
0.4 ~ 0.8). However, of course we have randomness from the metal
mixing, and hence a support from the theoretical side was also required.
Here, we recall the hamiltonian
H
dp
in Eq. (
8.3
). Using this hamiltonian, which
includes both the metal
d
z
2
and halogen
p
z
orbitals, we can treat the above three
insulator states appearing in Fig.
8.25
from a unified point of view. Among the
various terms in this hamiltonian, the readers may have a question about the e-l
coupling here. This coupling is indeed included in the second and fifth terms via the
site-dependent factors of
eðlÞ¼e
p
2
aðQ
lþ
1
Q
l
1
Þ
for odd
l
(halogen site) and
eðlÞ¼e
M
þ aðQ
lþ
1
Q
l
1
Þ
.
Before introducing the calculated results, we explain the meaning of these terms.
Let us think about the metal site. The contribution of the (
l
+ 1)th halogen to this
l
th
metal site is
for even
l
(metal site), and
VðlÞ¼V
dp
aðQ
lþ
1
Q
l
Þ
n
lþ
1
Þn
l
. We here emphasize
that we use a “hole picture,” namely, that the vacuum state is M
2+
and X
for the M
(X) site, respectively. When the halogen loses no electron, the expectation value of
n
lþ
1
remains almost zero and then the term roughly gives
þ aQ
lþ
1
n
l
aQ
lþ
1
n
l
n
lþ
1
¼ aQ
lþ
1
ð
1
aQ
lþ
1
n
l
, which is a part of
the fourth term of Eq. (
8.1
), with the reversed sign because of the hole picture. What
is interesting is the effective reduction of this effect in the presence of a hole at
the halogen site, namely,
hn
lþ
1
i
1. This is easily understood as the vanishing
Coulombic interaction between M and X
0
. We also have another type
of e-l interaction in the first term of Eq. (
8.3
) through the factor form of
tðlÞ¼t
dp
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