Theory of MX Chain Compounds - Material Designs and New Physical Properties in MX-and MMX-Chain Compounds - page 123

Exciton

M 3+ M 3+

STE

Complete inversion
of CDW phase at the
central two sites

Further
developed state

Fig. 8.10 Process to yield a soliton pair from the STE. The blue vertical arrows specify the
directions of the potential (lattice) changes. The green arrows mean the supposed electron
transitions

Δ Q=1

l =0 0

q o

q l (-1) l

0

- q o

Q=1
l > 0 0

Δ

l

Fig. 8.11 Staggered lattice displacements leading to the inversion of the CDW phase

panels, and obtain an enlarged region of the inverted phase. Now, if the readers
compare this fourth panel and that denoted by “ S + S ” in Fig. 8.9 , we notice that we
have made the same state. This is nothing but a soliton state, and in this case we
have made a pair of “charged solitons.” On the other hand, we also think about a
similar but slightly different state as denoted by “ S 0 S 0 ,” which is called a pair of
neutral solitons. Leaving the explanation why they are charged or neutral, we
proceed with our gedanken experiment. In the case of polarons, we think that an
electron and a hole in an exciton or in an STE will separate to each other. The
isolated electron and hole thus formed deform the lattice around themselves, but no
more invert the CDW state. As a more likely process, a free electron-hole pair will
also yield the polarons independently. In any case, we expect a polaron pair, P + P ,
as depicted in Fig. 8.9 (bottom panel).
From here on, we introduce a calculated result to demonstrate the validity of the
above idea [ 24 ]. In this calculation, we trace the ground and excited states based on
the following lattice configurations:

" ! ! #

l 0
2

þ DQ tanh j l l c j

l

q l ¼ q 0 ð 1 Þ 1 1 ; (8.22)

w