Theory of MMX-Chain Compounds - Material Designs and New Physical Properties in MX-and MMX-Chain Compounds - page 245

a

b

K MXM =0

U M =6

6

7

BCDW

U M

6

β

4

CDW

5

ACP

CP

4

AV

2

3

0 0.2 0.4 0.6 0.8 1

α

Fig. 12.6 Ground-state phase diagram of the 12-site model for K MXM ¼ 0(a) in the a - b - U M
space and (b) its cross section at U M ¼ 6. The parameters are t MM ¼ 1, t MXM ¼ 0.8, K MX ¼ 6,
V MM ¼ 0, V MXM ¼ 0, and V 2 ¼ 0[ 23 ]

model, we show how the on-site repulsion U M modifies the competition between
the , the AV phase appears.

As U M increases, all the phase boundaries are shifted to the large-

a and b terms in Fig. 12.6 . For small or moderate a and b

side, and
consequently the region of the AV phase is widened. This is because the on-site
repulsion U M favors uniform charge densities, while

b

the site-diagonal

electron-lattice coupling favors modulation of charge densities. Both terms

compete with each other. Then, the BCDW phase is realized only when the

b

b
term is strong enough to dominate over the U M term. This competition is easily
understood in the unphysical limit of small ionic mass. In this limit, the lattice
displacements instantaneously follow the motion of electrons so that the

b term

2

gives an attractive interaction to shift U M to U M eff ¼ U M b =K MX . This equation

is derived from completing the squares with respect to variables y a , i and y b , i . In the
physical limit of large ionic mass, however, the lattice displacements are statically
shifted to form a bipolaron lattice, i.e., the BCDW phase when

is large enough.
The situation becomes different when the site-off-diagonal electron-lattice cou-
pling

b

a
terms do not always compete with each other. In fact, they sometimes cooperate
with each other when modulation of bond-charge densities is not accompanied with
large modulation of site-charge densities [ 26 - 28 ]. That is why the phase boundaries
are not shifted to the large-

a increases. It favors modulation of bond-charge densities. The U M and

a side, but to the large- b side, when U M increases. When

a is large enough, the ACP phase is realized by modulating the distances between

the neighboring binuclear units.