Chemistry Reference
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Fig. 8.6 Comparison of the
optical conductivity spectrum
calculated by the HF
approximation and a
schematic picture of the
measured spectrum. In the
case of PtCl,
E
p
is around
2.7 eV
Measurement
HF result
?
0
1
2
3
4
5
6
7
8
Ep
Energy (eV)
8.2.2 Optical Properties
In this subsection, we discuss the optical properties of the CDW systems. As is
introduced in the experimental section, a prominent feature in the absorption
spectra is the strong absorption band whose intensity is more or less concentrated
at the lower edge, as schematically illustrated in Fig.
8.6
(right panel). Moreover,
the band takes the form of an asymmetric Lorentzian. These features are hard to
explain solely by the HF calculation shown in the previous subsection. In fact, The
HF calculation gives a broad absorption band extending from the HF gap to the
excitation energy from the bottom of the valence band to the top of the conduction
band (see the left panel of Fig.
8.6
).
Iwano et al. thought that this discrepancy came from the effect beyond the HF
approximation, namely, the exciton effect, and investigated it [
18
]. To start such a
calculation, it will be convenient to separate the original hamiltonian in Eq. (
8.2
)
into its HF part and the remaining part:
H
ePH2
¼ H
ePH2
;
HF
þ DH:
(8.14)
DH
in terms of the basis set that we constructed in the
HF calculation. As the first step, we rewrite the fluctuating part
Our task is then to express
DH
as
DH ¼ U
X
l
ðn
l"
hn
l"
iÞðn
l#
hn
l#
iÞ þ V
X
l
ðn
l
hn
l
iÞðn
lþ
1
hn
lþ
1
iÞ
þ V
X
ls
:ÞV
X
ls
ðhC
lþ
1
s
C
ls
iC
ls
C
lþ
1
s
þ
jhC
lþ
1
s
C
ls
ij
2
h.c
:
(8.15)
Here, we assume that the mean field in the brackets are already adjusted self-
consistently. We then insert
C
ls
¼
P
ms
f
ms
ðlÞC
ms
, and rearrange the terms, keeping
in mind
hC
lþ
1
s
C
ls
i¼S
0
ms
f
ms
ðl þ
2
and
S
0
means the
summation over all the occupied states). From here on, we use the notation that
hn
l
i¼S
0
ms
f
ms
ðlÞ
1
Þf
ms
ðlÞ
(
m
and
i
are the unoccupied and occupied one-electron states, respectively. The results
of the rearrangement are rather lengthy, so we only summarize their basic results. If
we call the states like
C
ms
C
is
jF
0
i
is the HF ground
state), they constitute a subspace of bare one-electron-excited states (see Fig.
8.7a
).
particle-hole excitations (
jF
0
i
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