Theory of MX Chain Compounds - Material Designs and New Physical Properties in MX-and MMX-Chain Compounds - page 132

broadening. The actual peak width, on the other hand, is very small, for example, as
small as 7 meV in [Ni(chxn) 2 Br]Br 2 [ 35 ]. This value presents a sharp contrast to
that in PtCl, which is approximately 300 meV. Although such a small width would
suggest an almost zero e-l interaction, we do not agree with that idea, since the Ni
compounds are also ionic crystals accompanied by relatively strong or intermediate
Coulombic interaction.
To solve this paradox, let us think about another doublon-holon model [ 36 ],
which is extended to include the e-l interaction:

H dhl ¼t 0 X
l

:Þt 0 X
l

:ÞþV X
l

ðd lþ 1 d l þ ðh lþ 1 h l þ n ðd l n ðhÞ h.c h.c

lþ 1

S X
l

ÞþS 2 X
l

ðq lþ 1 q l Þðn ðdÞ n ðhÞ

l

q 2

l ;

(8.25)

l

where the newly added terms, the fourth and fifth terms, describe the doublon/
holon-lattice interactions and the elastic energy, respectively. Of course, this form
of interactions between the doublon/holon and the lattice are directly related to the
original form of the e-l interaction. In the following, we discuss the case of one
doublon for simplicity, because it is essentially the same even in the doublon-holon
case. In the former case, the hamiltonian is reduced to a simpler form as

H dl ¼t 0 X
l

:ÞS X
l

2 X
l

S

ðd lþ 1 d l þ ðq lþ 1 q l Þn ðdÞ q 2 h.c þ

l :

(8.26)

l

In a sense, this is a very simple problem that includes only one particle and a
classical lattice. At a glance, this looks similar to a popular model called the
Holstein model [ 37 , 38 ], which will be expressed as

H Hols ¼t 0 X
l

:ÞS X
l

2 X
l

S

ðd lþ 1 d l þ q l n ðdÞ q 2

h.c þ

l :

(8.27)

l

For the Holstein model, it well known that even infinitesimally weak interaction,
S , makes a binding state, namely, the so-called polaron in one-dimensional systems.
Meanwhile, in the model of H d - l , a simple analysis of lattice optimization in the
presence of one doublon reveals that there is a critical value to form a bound state.
Although this fact seems to be against the “common sense” that there always exists
a bound state in one-dimensional systems, the mechanism is easily understood by
converting the model into its momentum representation:

2 t 0 X
k

X

2 X
p

S

ðkÞd k d k þ gðpÞd kþp d k q p þ

2

H dl ¼ cos jq p j ; (8.28)

k;p