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Fig. 12.4 Second-order
processes with respect to t MM
and t MXM in the CDW and CP
t MM
t MM
Though the effects of the long-range interactions are discussed later, it is here noted
that V MM increases the energy of the CDW phase and stabilizes the CP phase. The
second-order processes with respect to t MM shown in Fig. 12.4 lower the energy by
2 t MM 2 / U M in the CDW phase and by t MM 2
in the CP phase. That is why the
CDW phase is relatively stable for large
and the CP phase for large U M .Ina
similar manner, the effect of t MXM can be discussed from the second-order pertur-
bation theory. It does not affect the relative stability between the CDW and CP
phases. That is why the phase boundary is insensitive to t MXM . It is noted that, if the
long-range interactions are included, the second-order terms with respect to t MXM
for the CDW and CP phases become different. Even in such a case, the phase
boundary is more sensitive to t MM .
Experimentally, the ground states of K 4 [Pt 2 (pop) 4 X] n H 2 O with X
Cl, Br and
n ¼
2, 3 are shown to be in the CDW phase [ 1 - 4 ]. In general, when the halogen X
ion is either Cl or Br, so far all the ground states are known to be in the CDW phase.
For X
Cl and Br, the X p z level is so deep that the effective nearest-neighbor
transfer integral t MXM mediated by charge transfers through the X p z orbital is
small. Meanwhile, the site-diagonal electron-lattice coupling
is large owing to
the short distance between the neighboring M and X ions, d MX . Thus, the CDW
phase for X
Cl and Br is understood from the dominance of the electron-lattice
over electron-electron interactions other than the on-site repulsion U M ,
which is strong enough to suppress a phase with bipolarons discussed later.
In R 4 [Pt 2 (pop) 4 X] n H 2 O with X
I, depending on the cation R and on the
number of water molecules n , three electronic phases are suggested to appear: the
AV phase, the CDW phase, and the CP phase in the order of increasing of d MXM [ 7 ].
Though we have not obtained a phase diagram with the CDW phase between the
other two, we believe that, for small d MXM , the effect of t MXM is larger than those
of various interactions so that the larger t MXM stabilizes the AV phase. Meanwhile,
for intermediate to large d MXM , the competition between the electron-lattice
and electron-electron interactions discussed here and/or the competition between
the short- and long-range electron-electron interactions discussed later determine
the relative stability between the CDW and CP phases. As d MXM increases, the site-
diagonal electron-lattice coupling
becomes weak, while the on-site repulsion
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