Theory of MMX-Chain Compounds - Material Designs and New Physical Properties in MX-and MMX-Chain Compounds - page 241

a b K MXM =

6

U M =6

6

β

CDW

U M

4

CP

4

2

AV

0

2

0 0.2 0.4 0.6 0.8 1

t MXM

Fig. 12.3 Ground-state phase diagram of the 12-site model for infinitely large K MXM (a) in the
t MXM - b - U M space and (b) its cross section at U M ¼ 6. The parameters are t MM ¼ 1, a ¼ 0,

K MX ¼ 6, V MM ¼ 0, V MXM ¼ 0, and V 2 ¼ 0[ 23 ]

competition among the charge-ordered phases until later, we simply ignore the
long-range interactions. Exactly diagonalizing the present model, we show a phase
diagram in the space spanned by t MXM , b , and U M in Fig. 12.3 , where t MM is set to

2

be unity. Because the parameter sets ( a , b , K MX , K MXM ) and ( la , lb , l K MX ,

2

l K MXM ) are related by the scaling of y a , and y b and thus equivalent, the specific

value of K MX is insignificant. First of all, t MXM is found to stabilize the AV phase. In
R 4 [Pt 2 (pop) 4 I] n H 2 O, where electrons are the most delocalized among X Cl, Br,

and I, the AV phase may appear for small d MXM because t MXM is expected to
become large. Meanwhile t MXM does not much affect the boundary between the
CDW and CP phases.

¼

12.4 Electron-Lattice Versus Electron-Electron Interactions

In Fig. 12.3 , the CDW phase is stabilized by the site-diagonal electron-lattice
coupling , while the CP phase is stabilized by the on-site repulsion U M . Thus,

the competition between the electron-lattice and electron-electron interactions
determines the relative stability of these two charge-ordered phases. This fact is
easily understood with the help of the second-order perturbation theory from the
strong-coupling limit

b

0 . The energies of the CDW and CP
phases are degenerate in this limit as long as the long-range interactions are absent.
Namely, their energies are both given by

t MM ¼ t MXM ¼ a ¼

bjyjþU M þ K MX y 2 per binuclear unit.