Theory of MMX-Chain Compounds - Material Designs and New Physical Properties in MX-and MMX-Chain Compounds - page 248

12.8 Optical Conductivities in Different Electronic Phases

Here, we calculate the optical conductivity spectra, having R 4 [Pt 2 (pop) 4 I] n H 2 Oin
mind. We focus on the differences among the spectra in the AV, CDW, and CP
phases. We do not calculate the lattice displacements self-consistently but fix them
to be a constant, | y |

¼ y 0 , although we change the distortion pattern according to the
electronic phase. The elastic constants are then meaningless. The lattice
displacements are y a;i ¼ y b;i ¼

i y 0 in the
CDW phase, and y a;i ¼y b;i ¼ y 0 in the CP phase. The optical excitation processes
are schematically represented in Fig. 12.9 for the CDW and CP phases. The
illustration becomes realistic only near the strong-coupling limit. In this limit, the
excitation energies in the CDW phase are given by

0 in the AV phase, y a;i ¼ y b;i ¼ð 1 Þ

E CDW E CDW

MM ¼ U M V MM ; MXM ¼

2 bjyjV MM þ 2 V 2 ;

while those in the CP phase are given by

E C MM ¼ E C MXM ¼

2 bjyjþV MXM 2 V 2 ; 2 bjyjþV MM 2 V 2 :

Among the four energies, E MM CDW is much larger than the others because of the
strong on-site repulsion U M .
From the exact diagonalization of the present model, we show optical conduc-
tivity spectra in the three phases for U M ¼ 2 in Fig. 12.10a , for U M ¼ 4in
Fig. 12.10b , and for U M ¼

6 in Fig. 12.10c , with varying V MM and V MXM according
to the relations, V MM ¼ U M /2 and V MXM ¼ U M /4. As the electron-electron
interactions are not so weak, a single peak appears at a similar position in both of
the AV and CDW phases, while two peaks generally appear in the CP phase in the
energy range of the figures. The difference in the number of peaks between the
CDW and CP phases is due to the strong on-site repulsion U M , as discussed above.
We then focus on the CP phase and show the dependence of the energies and
intensities of the two excitations on the long-range interactions V MM and V MXM in
Fig. 12.11 . The lower energy E MM CP increases with V MXM , while the higher energy
E MXM CP increases with V MM , as expected from the strong-coupling analysis. The
excitation intensities are comparable when the energy difference is small. Mean-
while, the low-energy excitation is much stronger when the energy difference
is large.
In the optical experiments, so far all R 4 [Pt 2 (pop) 4 I] n H 2 O compounds have a
single peak below 3 eV [ 7 ]. Observation of a single peak is reasonable in the AV
and CDW phases because of the strong on-site repulsion U M . Meanwhile, observa-
tion of a single peak in the CP phase indicates that the nearest-neighbor repulsion
through an X site V MXM is substantially weaker than the nearest-neighbor repulsion
within the unit V MM . At least, the repulsion V MM is so strong as to stabilize the
CP phase.