- Email: [email protected]
Nonlinear optical response of MX chains in a one-band extended Peierls-Hubbard model
Synthetic Metals 86 (1997) 2231-2232
Nonlinear
Optical
Response of MX Chains in a One-Band Peierls-Hubbard Model
A. Saxena,
Extended
J. L. BrCdas’, and A.R. Bishop
Z. Shuai*,
Theoretical Division, MS B,?6.2, Los Alamos National Laboratory, Los Alamos, NM 87545, USA *Service de Chimie Mate’riaux Nouveaux, Universite’ de Mons-Hainaut, B-7000, Mons, Belgium We study both
the
nonlinear
optical (NLO) res p onse of quasi-one-dimensional
the electron-phonon
tight-binding
extended
absorption, a function
and electron-electron Peierls-Hubbard
(ii) electroabsorption of electronic
single configuration as conducting
intetaction
polymers.
case of MX chains.
The predicted
charge-density-wave
Keywords:
Models
These
NLO response
(CDW)
of non-linear
results
for relevant MX
phenomena,
-T~(&$l+l,o + H.c.1+ GChJr -
to low-dimensional
ql+l)nr,o
t-w C
!lt+U C
1
1
where (I/,, (al,,)
2
creates
w,+w,l
(annihilates)
+
V
C
n~,on~+l,cr’,
l,a,d
an electron
at site
1 with spin u, nl+, = a/,al,, is the number operator, T the hopping energy, b and V are on-site and nearestneighbor Hubbard terms, & is the electron-phonon coupling, w is the spring constant, and ql is the displacement at site 1. We write H = HHF + AH, where HHF is
0379-6779/97/$17.00 8 1997 Elsevier Science S.A. All rights reserved
PII SO379-6779(96)048 16-3
(xc3))
materials
here we apply
them
experimental
as
within such to the data
on
PtCl. optical
methods,
Electroabsorption.
is the mean-field Hartree-Fock part and the correlations AH are treated as a perturbation. Within the Hartree-Fock approximation, the U and V terms renormalize the non-interacting model in the following way: uv -- u~fii,-oC~,Cj,o HHF i,o
-
+V
VCpi,,(ctnCi+l,o +
h,q
i,o
C (fii,oni+~,d+ fii+l,o/ni,g), i,o,o’
where iii,, represents the average electron number at site i with spin 6. Here pi,, is the average bond order of electron with spin u for the bond linking sites i and i+ 1. When varying U and V, the bare parameters (T, S, w) are assumed to be unknown. However, we assume that the renormalized parameters give exactly the same mean-field results regardless of U and V. Then U and V give only the correlation effects. The fluctuation term (deviation from the mean-field approximation) is: nl,,nl,p 1
I,0
l,a
of (i) photoinduced systematically
with available
with
one-band,
susceptibility
is studied
AH = U c
H =
materials
l/2-filled,
variation optical
of parameters
is compared
Non-linear
Halogen-bridged mixed-valence transition metal linear chain complexes (or MX chains, M: Pt,Pd,Ni; X: CI,Br,I) are highly anisotropic, quasi-one-dimensional (QlD) materials with competing electron-phonon and electron-electron interactions [l]. There is considerable interest in the study of nonlinear optical (NLO) properties of quasi-one-dimensional materials [2]. Here we focus on the theoretical predictions based on a one-band model for NLO response of low dimensional electronic materials. Iwasa et al. [3] measured the third harmonic generation (THG) spectrum of PtCl and found a broad peak near 1.8 eV with a x c3) value around 3~10-‘~ esu, comparable to those in conjugated polymers [4]. They also found an enhancement in the 0.5 - 1.0 eV region. Sun et al. [5] have earlier tried to analyze the xc31 spectra. Wada and Yamashita [6] measured the electroabsorption spectra for PtCl and Iwano and Nasu [7] have previously attempted to analyze it. The one-band extended Peierls-Hubbard model is described by the Hamiltonian
U,V)
are generic
choice
material
the
nonlinear
parameters
electronic
using a discrete,
Specifically,
(iii) third-order
(Hubbard
(CI).
However,
the strong
model.
and
correlation
interactions
+ V c nl,anl+l,u’ l,O,O’
- HFF.
This term is treated within a single configuration interaction (SCI) method for varying U and V. The results for PtCl for representative parameters are shown in Figs. (l)-(3). The chain length is N=lOO sites. The energy (on the horizontal axis) is chosen in units of the hopping energy T=O.S eV). The scaled optical gap for the choice of parameters is -3.6T = 2.88 eV. In Fig. (1) we plot calculated photoinduced absorption relative to the bottom of the conduction band which shows a strong peak at -0.4eV above the band edge. There is some structure up to 1.5 T.
2232
A. Sarena et al. /SyntheticMetals
200.0
86 (1997) 2231-2232
Electroabsorption (EA) is an important measurement for photo-refractive materials that provide many
Photoinduced absorption
nonlinear optical applications. tion difference spectrum [Aa
N-100 150.0 .
obtain
tion
wvI_,
0.0 0.0
1.0
2.0
3.0
IT
FIG. 1. Photoinduced
absorption
in PtCl;
T=0.8
eV.
Electroabsorption N-100,
u=2. VPO.75 so.5
4.0
3.0 Fr-
2. Electroabsorption
0
in PtCl;
T=0.8
eV.
20000.C
‘I
THG (N=lOO,U=2,V=0.75,0.9/0.1)
WOO.0
5000.0
0.0 ’ 0.5
Eh
the symmetry and allows bidden transition. Figure
50.0
l!xmo.0
theoretical
the absorp = Q(W, F)-cu(ti, 0)] to
where
F is the electric
field.
Unlike linear absorpticn the even-parity excitonic stat,e can be detected in EA because the applied field breaks
100.0 :, -
FIG.
the
We calculate
1.5
2.5
Fund. Frequency (-I-)
FIG. 3. Third harmonic generatio (THG) with T=0.8 eV and broadening = 0.05.
spectra
for PtCl
spectra.
The
the (previously) optically for(2) depicts the electroabsorp
oscillatory
structure
above
4.0 T is
due to the conduction band st’ates. The pronounced feature between 3.0 and 4.0 T is due to an exciton. In Fig. (3) we we show the third order nonlinear susceptibility ~(~1. We have used an appropriate (0.05) broadening factor. There are two sets of peaks. The big peak at 1.2 T is a lB, stat,e due to a three-photon resonance and the small peak at I.4 T is a three-photon resonance with the conduction band continuum. The peak at 2.05 T arises from a two-photon resonance of an m,4, state and the shoulder at 2.15 T is a two-photon resonance with the continuum states. The above results lead to t.he following interpretation of the energy levels in terms of increasing energy: lA, (ground stat,e), lB, (exciton), m,4, (even parity state) and the band continuum. The estimat.ed binding energy of the excit,on is -0.35 eV. We also studied the systematic effect of [J and V variation on the EA and X(3) spectra. We believe that these st.udies can elucidate the role of low-lying electronic escitations in various higher order optical processes in QlD systems: in particular the distinct.ion bet.ween band and excit,on descriptions, photoinduced charge transfer, PL and EL, etc. In conclusion, the above results qualitatively explain the observed NLO features of PtCl in experiments [3,6] and point to an excitonic behavior. They are also consistent with the t,wo-band model results since PtCl is a very localized CDW material. We believe that two photon absorption (e.g. z-scan) experiments can further clarify t.he relative energy of excited states in PtCl. This work was supported by the U.S. DOE and by the Belgian National Fund for Scientific Research. PI J. T. Gammel et al., Phys. Rev. B 45, 6408 (1992). [21 D. S. Chemla and J. Zyss (eds.) Nolinear Optical Properties of Organic Molecules and Crystals (Academic, New York, 1987). [31 Y. Iwasa et al. Mol. Cryst. Liq. Cryst. 217, 37 (1992); Appl. Phys. Lett. 59. 2719 (1991). 141 J. L. BrCdas et al., Chem. Rev. 94, 243 (1994). [51 X. Sun et al., Synt,h. Metals 57, 3986 (1993); Synth. Metals 71, 1683 (1995). PI Y. Wada and M. Yaw&ha, Phys. Rev. B 42, 7398 (1990). PI K. Iwano and K. Nasu in Relazation in Polymers, ed. T. Kobayashi (World Scientific, Singapore, 1993), p. 245.
Nonlinear
Optical
Response of MX Chains in a One-Band Peierls-Hubbard Model
A. Saxena,
Extended
J. L. BrCdas’, and A.R. Bishop
Z. Shuai*,
Theoretical Division, MS B,?6.2, Los Alamos National Laboratory, Los Alamos, NM 87545, USA *Service de Chimie Mate’riaux Nouveaux, Universite’ de Mons-Hainaut, B-7000, Mons, Belgium We study both
the
nonlinear
optical (NLO) res p onse of quasi-one-dimensional
the electron-phonon
tight-binding
extended
absorption, a function
and electron-electron Peierls-Hubbard
(ii) electroabsorption of electronic
single configuration as conducting
intetaction
polymers.
case of MX chains.
The predicted
charge-density-wave
Keywords:
Models
These
NLO response
(CDW)
of non-linear
results
for relevant MX
phenomena,
-T~(&$l+l,o + H.c.1+ GChJr -
to low-dimensional
ql+l)nr,o
t-w C
!lt+U C
1
1
where (I/,, (al,,)
2
creates
w,+w,l
(annihilates)
+
V
C
n~,on~+l,cr’,
l,a,d
an electron
at site
1 with spin u, nl+, = a/,al,, is the number operator, T the hopping energy, b and V are on-site and nearestneighbor Hubbard terms, & is the electron-phonon coupling, w is the spring constant, and ql is the displacement at site 1. We write H = HHF + AH, where HHF is
0379-6779/97/$17.00 8 1997 Elsevier Science S.A. All rights reserved
PII SO379-6779(96)048 16-3
(xc3))
materials
here we apply
them
experimental
as
within such to the data
on
PtCl. optical
methods,
Electroabsorption.
is the mean-field Hartree-Fock part and the correlations AH are treated as a perturbation. Within the Hartree-Fock approximation, the U and V terms renormalize the non-interacting model in the following way: uv -- u~fii,-oC~,Cj,o HHF i,o
-
+V
VCpi,,(ctnCi+l,o +
h,q
i,o
C (fii,oni+~,d+ fii+l,o/ni,g), i,o,o’
where iii,, represents the average electron number at site i with spin 6. Here pi,, is the average bond order of electron with spin u for the bond linking sites i and i+ 1. When varying U and V, the bare parameters (T, S, w) are assumed to be unknown. However, we assume that the renormalized parameters give exactly the same mean-field results regardless of U and V. Then U and V give only the correlation effects. The fluctuation term (deviation from the mean-field approximation) is: nl,,nl,p 1
I,0
l,a
of (i) photoinduced systematically
with available
with
one-band,
susceptibility
is studied
AH = U c
H =
materials
l/2-filled,
variation optical
of parameters
is compared
Non-linear
Halogen-bridged mixed-valence transition metal linear chain complexes (or MX chains, M: Pt,Pd,Ni; X: CI,Br,I) are highly anisotropic, quasi-one-dimensional (QlD) materials with competing electron-phonon and electron-electron interactions [l]. There is considerable interest in the study of nonlinear optical (NLO) properties of quasi-one-dimensional materials [2]. Here we focus on the theoretical predictions based on a one-band model for NLO response of low dimensional electronic materials. Iwasa et al. [3] measured the third harmonic generation (THG) spectrum of PtCl and found a broad peak near 1.8 eV with a x c3) value around 3~10-‘~ esu, comparable to those in conjugated polymers [4]. They also found an enhancement in the 0.5 - 1.0 eV region. Sun et al. [5] have earlier tried to analyze the xc31 spectra. Wada and Yamashita [6] measured the electroabsorption spectra for PtCl and Iwano and Nasu [7] have previously attempted to analyze it. The one-band extended Peierls-Hubbard model is described by the Hamiltonian
U,V)
are generic
choice
material
the
nonlinear
parameters
electronic
using a discrete,
Specifically,
(iii) third-order
(Hubbard
(CI).
However,
the strong
model.
and
correlation
interactions
+ V c nl,anl+l,u’ l,O,O’
- HFF.
This term is treated within a single configuration interaction (SCI) method for varying U and V. The results for PtCl for representative parameters are shown in Figs. (l)-(3). The chain length is N=lOO sites. The energy (on the horizontal axis) is chosen in units of the hopping energy T=O.S eV). The scaled optical gap for the choice of parameters is -3.6T = 2.88 eV. In Fig. (1) we plot calculated photoinduced absorption relative to the bottom of the conduction band which shows a strong peak at -0.4eV above the band edge. There is some structure up to 1.5 T.
2232
A. Sarena et al. /SyntheticMetals
200.0
86 (1997) 2231-2232
Electroabsorption (EA) is an important measurement for photo-refractive materials that provide many
Photoinduced absorption
nonlinear optical applications. tion difference spectrum [Aa
N-100 150.0 .
obtain
tion
wvI_,
0.0 0.0
1.0
2.0
3.0
IT
FIG. 1. Photoinduced
absorption
in PtCl;
T=0.8
eV.
Electroabsorption N-100,
u=2. VPO.75 so.5
4.0
3.0 Fr-
2. Electroabsorption
0
in PtCl;
T=0.8
eV.
20000.C
‘I
THG (N=lOO,U=2,V=0.75,0.9/0.1)
WOO.0
5000.0
0.0 ’ 0.5
Eh
the symmetry and allows bidden transition. Figure
50.0
l!xmo.0
theoretical
the absorp = Q(W, F)-cu(ti, 0)] to
where
F is the electric
field.
Unlike linear absorpticn the even-parity excitonic stat,e can be detected in EA because the applied field breaks
100.0 :, -
FIG.
the
We calculate
1.5
2.5
Fund. Frequency (-I-)
FIG. 3. Third harmonic generatio (THG) with T=0.8 eV and broadening = 0.05.
spectra
for PtCl
spectra.
The
the (previously) optically for(2) depicts the electroabsorp
oscillatory
structure
above
4.0 T is
due to the conduction band st’ates. The pronounced feature between 3.0 and 4.0 T is due to an exciton. In Fig. (3) we we show the third order nonlinear susceptibility ~(~1. We have used an appropriate (0.05) broadening factor. There are two sets of peaks. The big peak at 1.2 T is a lB, stat,e due to a three-photon resonance and the small peak at I.4 T is a three-photon resonance with the conduction band continuum. The peak at 2.05 T arises from a two-photon resonance of an m,4, state and the shoulder at 2.15 T is a two-photon resonance with the continuum states. The above results lead to t.he following interpretation of the energy levels in terms of increasing energy: lA, (ground stat,e), lB, (exciton), m,4, (even parity state) and the band continuum. The estimat.ed binding energy of the excit,on is -0.35 eV. We also studied the systematic effect of [J and V variation on the EA and X(3) spectra. We believe that these st.udies can elucidate the role of low-lying electronic escitations in various higher order optical processes in QlD systems: in particular the distinct.ion bet.ween band and excit,on descriptions, photoinduced charge transfer, PL and EL, etc. In conclusion, the above results qualitatively explain the observed NLO features of PtCl in experiments [3,6] and point to an excitonic behavior. They are also consistent with the t,wo-band model results since PtCl is a very localized CDW material. We believe that two photon absorption (e.g. z-scan) experiments can further clarify t.he relative energy of excited states in PtCl. This work was supported by the U.S. DOE and by the Belgian National Fund for Scientific Research. PI J. T. Gammel et al., Phys. Rev. B 45, 6408 (1992). [21 D. S. Chemla and J. Zyss (eds.) Nolinear Optical Properties of Organic Molecules and Crystals (Academic, New York, 1987). [31 Y. Iwasa et al. Mol. Cryst. Liq. Cryst. 217, 37 (1992); Appl. Phys. Lett. 59. 2719 (1991). 141 J. L. BrCdas et al., Chem. Rev. 94, 243 (1994). [51 X. Sun et al., Synt,h. Metals 57, 3986 (1993); Synth. Metals 71, 1683 (1995). PI Y. Wada and M. Yaw&ha, Phys. Rev. B 42, 7398 (1990). PI K. Iwano and K. Nasu in Relazation in Polymers, ed. T. Kobayashi (World Scientific, Singapore, 1993), p. 245.