Theory of MX Chain Compounds - Material Designs and New Physical Properties in MX-and MMX-Chain Compounds - page 126

a

S -

0 0 0 0

2 2 2 2

0

0 2 0 2 0 2 2

S -

b

S

0

0

0 2 0 1 2 0 2

0 2 0 2 0 1 2 0

S 0

Fig. 8.16 Illustration to explain how to count soliton charges. (a) A charged soliton case and
(b) a neutral soliton case. The numbers are the electron occupancies at each metal site

Finally, we discuss possible processes expected from these results of the adia-
batic potential surfaces. Looking at Fig. 8.14 or Fig. 8.15 , we judge that the charged
soliton pair is unlikely to be formed using the same path as that the STE follows,
since the former has a higher energy than the latter, as is already mentioned. Such a
situation does not support the idea of a short life time of the STE due to the charged
solitons. Of course we cannot completely exclude another possibility that the
energy of the charged-soliton pair is lower than that of the STE. However, in our
opinion, it is against a relatively large U value that is naturally deduced from a large
V value. Here, it is emphasized that we need the latter to have the strong exciton
effect. In turn, what about the possibility of forming the neutral solitons? We think
that it has plenty of chances. We here mention two scenarios. One is the path within
the singlet channel. In this case, it is a nonadiabatic transition from S 2to S 1, as
indicated by the wavy like in Fig. 8.15 . Although a realistic calculation has not been
performed yet, a prototype calculation predicts that appropriate inclusion of phonon
modes will enhance the transition probability up to a realistic value, for example,
several 10 ps as a life time of the STE [ 25 ]. The other scenario is based on a
singlet-triplet conversion. Actually, Fig. 8.15 shows a downhill course on the T 1
surface from the STE to the neutral-soliton pair. In this case, we need a sufficiently
large singlet-triplet conversion rate and it is not unrealistic because Pt is a heavy
atom.
In the rest of this subsection, we discuss the charge-spin property of a soliton.
The soliton has its own charge and spin even though it is a composite particle made
of several electrons. Regarding the spin, it will be easier to see. Just looking at
Fig. 8.9 once more, we immediately notice an unpaired spin at each site of S 0 .We
therefore state in confidence that the neutral solitons have a spin 1/2. Similarly, we
see that all the spins are paired in S , and so the charged solitons have no spin
degree of freedom.
On the other hand, the charge will be difficult to imagine, because we have
undulation of charge density in the background. We hence use the method to count
the charge as described in Fig. 8.16 . Namely, we calculate the change in the electric
dipole moment before and after the movement of the soliton. For example, in the
case of the charged soliton, we shift the soliton by one unit cell, i.e., 2 a ,asin
Fig. 8.16a ( a is the distance between the neighboring metal ions). If we define the
soliton charge as Q S , the change in the dipole moment is 2 aQ S . This should be