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12.11 CDW-to-CP Transition
Starting from the metastable CDW phase inside the hysteresis loop, we find a
transition to the stable CP phase for
< b c . Because the delocalization
tendency is weak, the 48-site chain is enough to derive the present conclusions.
When three electrons are excited, the CDW order is partially destroyed and the CP
order appears instead, but most of the regions remain in the CDW phase. When four
electrons are excited, microscopic CDW domains survive only for a while, and the
CDW domain is almost completely destroyed. After they disappear, CP domains
appear. On average, they grow and mostly cover the system at last. A threshold
exists in the photoexcitation intensity roughly between three- and four-electron
excitations for the 48-site chain. When more electrons are excited, the CDW
domain quickly disappears, and CP domains appear and grow to be merged into a
single CP domain covering the system. Whether the transition is completed or not
actually depends on the choice of random numbers initially added to the lattice
variables. The threshold should be understood in a statistical manner for finite-size
The threshold intensity sensitively depends on the relative stability of the two
phases. For
b ¼
b c , we find the CDW phase still metasta-
ble, and the energy difference from the stable CP phase is enlarged. The threshold
intensity is greatly reduced: one-electron excitation in the 48-site chain is sufficient for
the transition to the CP phase. For
b ¼
4.0, which is much below
5.0, where the CDW phase is almost
degenerate with the CP phase, the transition is not easily realized. Intensive excitations
only destroy the CDW order, and they do not produce any charge-lattice order.
This dependence of the threshold intensity can be understood by drawing
diabatic potentials in the CDW and CP phases. After the photoexcitation, the excess
energy is quickly distributed to the surroundings, and the coherence is lost under
thermal fluctuations. For the proliferation of new domains, the processes after the
coherence is lost are more important than the process just after the photoexcitation.
Since the electronic states in the MMX compounds with ligand pop are well
described from the strong-coupling viewpoint [ 23 ], spatially local pictures are
helpful. Then, we consider the diabatic potentials in the CDW and CP phases for
the 4-site system, in which the binuclear unit on sites 1 and 2 are coupled with the
other on sites 3 and 4 (Fig. 12.12 ):
H 4 site ¼t MM X
b ¼
ðc 1 ;s c 2 ;s þ
: þ c 3 ;s c 4 ;s þ
ðc 2 ;s c 3 ;s þ
þbu 1 ðn 3 n 2 ÞþU M X
n i;" n i;# þ K MX u 1 þðM 2
= Þ u 1 :
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