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In-Depth Information
V
MM
=2
V
MM
=3
a
b
CP
CP
E
MXM
E
MM
V
MXM
=
E
MXM
E
MM
3.0
V
MXM
=2.0
2.5
1.5
2.0
1.5
1.0
1.0
0.5
0.5
0
0
1
2
3
1
2
3
ω
ω
Fig. 12.11 Optical conductivity in the CP phase of the 12-site model, as a function of
V
MXM
for
(a)
V
MM
¼
2 and (b)
V
MM
¼
3. The parameters are
t
MM
¼
1,
t
MXM
¼
0.8,
a ¼
0.2,
b ¼
4,
y
0
¼
0.1,
U
M
¼
6, and
V
2
¼
0[
23
]
CDW and CP phases, than the nearest-neighbor repulsion within the unit
V
MM
.
Furthermore, we reasonably expect that the next-nearest-neighbor repulsion
V
2
is
smaller than
V
MXM
. Therefore, we can derive the relation
E
CDW
<E
C
MM
, which is
consistent with the observed energy difference between the CDW and CP phases.
This relation is intuitively understood in the following way. In the CDWphase, holes
reside at M
3+
M
3+
units. By any charge-transfer process, the hole pair in a unit is so
separated that an electron and a hole attract each other by the amount of
V
MM
. In the
CP phase, however, holes are so located that the distance between the neighboring
holes is the largest among the possible electronic configurations. By any charge-
transfer process, some holes approach each other, so that it costs repulsive energy.
MXM
12.9 Summary of Ground-State Properties
Different electronic phases appear in R
4
[Pt
2
(pop)
4
I]
n
H
2
O, depending on the coun-
terion and on the number of water molecules. It is suggested from experiments that
the electronic phases are classified according to the distance between the neighbor-
ing binuclear units
d
MXM
[
7
]. The CP phase is suggested to appear for large
d
MXM
,
while the CDW phase is realized for small
d
MXM
. The relative stability between the
two phases is determined by a combined effect of competition between
electron-lattice and electron-electron interactions and competition between short-
and long-range electron-electron interactions. As
d
MXM
decreases, the site-
diagonal electron-lattice interaction and long-range electron-electron interactions
become larger, and their effects become dominant over the effect of the short-range
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