- Email: [email protected]
Polaron excitations in doped C60 and C70
3202
Synthetic Metals, 55-57 (1993) 3202-3207
POLARON EXCITATIONS IN DOPED C60 AND C70
Kikuo HARIGAYA Fundamental Physics Section, Electrotechnical Laboratory, Tsukuba, Ibaraki 305 (Japan)
ABSTRACT We propose a Su-Schrieffer-Heeger type electron-phonon model for fullerenes: C60 and C70. The model is solved by a numerical iteration method with applying the adiabatic approximation to phonons. When the system (C60 or C70) is doped with one or two electrons (or holes), the additional charges wccumulate along almost an equatorial line of the molecule. The dimerization becomes weaker along almost the same line. Two energy levels, the occupied state and the empty state, intrude largely in the gap. The intrusion is larger in C70 than in C60. These are "polarons" in doped fuUerenes. It is also found that C60 and C70 are related mutually with respect to electronical structures as well as lattice geometries. We also calculate optical properties of C60. In optical absorption of the doped C60, there is a new peak at lower energy than those of the intergap transition peaks. The third harmonic generation of the neutral C~0 in low frequencies agrees with experiments. Relations of polarons with recent experiments are pointed out.
INTRODUCTION AND SUMMARY Recently, the fullerenes C~ have been intensively investigated. Here, we review the recent investigation of a single C60 or C70 molecule, and discuss lattice distortion and reconstruction of electronic levels upon doping. We have described C60 and CT0 as an electron-phonon system and have extended the Su-Schrieffer-Heeger (SSH) model [1] of conjugated polymers. We have calculated for systems where one or two electrons are added or removed. We shall discuss properties of "polarons" in fullerenes, which have been reported in detail in [2-4]. We have found that sites, where additional charges are prone to accumulate, are common to C60 and CT0. They are along the equatorial line in C60. In this regard, we should bear in mind that C70 is made from C~0, by division into two parts and adding ten carbons. It is quite 0379-6779/93/$6.00
© 1993- Elsevier Sequoia. All rights reserved
3203
interesting that there are relations of electronical properties as well as the structural relation between (doped as well as undoped) Cs0 and C70. We have calculated the optical properties of C60 [4,5]. The optical transition between the HOMO and LUMO of the neutral C60 is dipole forbidden [4]. The lowest energy of the peaks of the optical absorption spectrum is about 2.9eV. When doped with additional charges, a new peak appears (at 0.7eV for electron doping and at 1.0eV for hole doping) due to the allowed transition [4]. The nonhnear optical susceptibility (third harmonic generation (THG)) of the neutral Cs0 has been calculated [5]. The magnitudes, 10 - n esu at the lowest three photon resonance and 10 -12 esu at the off resonance, agree well with experiments. We have obtained a very large peak about 10 -1° esu at 3w ,-~ 6eV owing to the double resonance enhancement. MODEL We have used the following model which is an extension of the SSH model [1] of conjugated polymers: K
2
n = ~ (-to + ~y,,,)(cLc,,. + h.c.) + 7 ~ Y'"" (,,~) (i,:),a
(1)
Here, a is the electron-phonon coupling, y,,j is the bond variable which measures the magnitude of the dimerization of the bond between the i- and j-th sites, the sum is taken from over all the nearest neighbor pairs (i,j), and K is the spring constant. This model has been applied to the geometries of Cs0 and Cr0, and solved by the adiabatic approximation. The full lattice relaxation has been realized by a numerical method shown in [4]. POLARONS IN C60 AND Cr0 We have taken to = 2.5eV, because a tight binding model with the same v~lue well reproduces the band structure of a two-dimensional graphite plane [6]. The same value has been used in polyacetylene [1]. Two quantities, c~ = 6.31eV/~
and K = 49.7eV//~ 2, have
been determined so that the length difference between the short and long bonds in C60 is the experimentally observed value: 0.05~[7]. Here, the dimensionless electron phonon coupling
~ Fig. 1. Lattice structures of doped
D
E
Cno [(a) IN¢I = 1 and (b) INcl = 2] and (c) neutral C7o
3204
A =_ 2a2/TrKto has been taken as 0.2 as in polyacetylene [1]. The number of electrons Nel has
been varied within - 2 < Nc _< 2, where Nc = N,i - N, and N is the number of carbon atoms. First, we discuss lattice and electronic structures of Cs0 [2,4]. The lattice configurations of the doped systems are shown in Fig. l(a) and (b). We show three kinds of the shorter bonds. The shortest bonds, d, are represented by the thick lines. The second shortest ones, b, are shown by the usual double lines. The dashed lines indicate the third shortest bonds. They are the bonds f in Fig. l(a) and bonds g in Fig. l(b). Other longer bonds are not shown. The figures are the same for the electron and hole dopings. When the change in the number of electrons is one, the change in the electron density is the largest at the sites at the ends of dashed lines, namely, points D. The dashed lines are mostly located along an equatorial line of C60. The absolute value of the length of the bonds g is the smallest of the four kinds of bonds with negative bond variables. The dimerization becomes the weakest along this equatorial line. The distortion of the lattice is similar to that of a polaron [8] in conjugated polymers; the spatial phase of the alternation of short and long bonds does not change upon doping, and the lattice distortion is the largest (the dimerization is the weakest) where the change in the local electron density is the largest. When the change in the electron number is two, configurations of dashed lines along the equatorial line change, as shown in Fig. l(b). The ordering of bonds, f and g, with respect to the bond variable is reversed. Other configurations are the same. The change in the electron density is also the largest at points D. Therefore, polaronic distortion persists when the doping proceeds from one to two electrons (or holes). This can be compared with a bipolaron formation in undegenerate conjugated polymers [8]. Next, we look at changes in the electronic level structures. When the system is doped, the degeneracy decreases due to the reduced symmetry. This reduction comes from the deformation of the lattice. This is one of the Jahn-Teller distortions. The removal of the degeneracies of energy levels is due to the Hg distortion [9]. When [N~[ = 1 and 2, the highest level, which splits from the HOMO of the neutral system, is undegenerate. Its energy shifts upward. In contrast, the other two leveLs shift only slightly. Similarly, the LUMO of the neutral system splits into two levels. The energy of the undegenerate level shifts downward, while change of the energy of the doubly degenerate level is small. This change in the level structures is common to two cases of the electron and hole dopings. The change is similar to that in the polaron formation [8] in conjugated polymers. We discuss changes in lattice structures and electron distributions of the doped Cr0 [3,4]. The dimerization strengths change their values mostly along the ring-like part of the molecule, while the patterns with the mirror reflection symmetry persist. Change in electron density at sites E is very small. This is a consequence of the fact that dimerization almost disappears along bonds f and g. The property of the part along the equatorial line is similar to that of the graphite plane. The strengths of the dimerization change largely along bonds, from a to e, upon doping. The additional charges tend to accumulate near these bonds. The positions D, where the additional charges accumulate most densely, correspond to the sites D of C60. When
3205
we make Cz0 from C60, sites E are added in the interval, but the property, by which additional charges tend to accumulate at sites D, persists for C70. This finding is quite interesting. We discuss structures of electronic energy levels. When the system is doped with up to two electrons or holes, the HOMO and LUMO of the neutral system largely extend into the gap. The positions of the other levels change only slightly. The magnitude of level intrusion is larger than that in C60 due to nondegenerate levels near the gap at Nc = 0. The HOMO and LUMO of the neutral system have large amplitude at sites, from A to D. The amplitude at D is the largest. The amplitude at E is very small. Therefore, the additional charge is prone to accumulate most at sites D. OPTICAL PROPERTIES We discuss how the "polarons" in C60 would be observed in optical absorption [4]. In the neutral C60, the transition between the HOMO and the LUMO (,-~ 2eV) is dipole forbidden and does not appear. In electron-doped C60, there appears a new peak at low energy (,,,0.7eV). This peak corresponds to the transition between the singly occupied molecular orbitM and the next lowest unoccupied molecular orbital, etc., when Nc = 1. It corresponds to the transition between the LUMO and the next lowest unoccupied molecular orbital, etc., when Nc = 2. Therefore, the new peak at low energy is due to the splitting of the LUMO. Similarly, the new peak appears at about leV in hole doped C60. Next, we look at spectral dispersions of the THG of the neutral C60 [5]. We display the absolute value in Fig. 2. In the bottom of the figure, we show the energies of the dipole allowed
I
0
4 i
i
III
allowed
I lil ILl '1 I I1' IIII
II
forbidden I
(eV)
I
I
I
Ill III
Fig. 2. Dispersion of third harmonic generation of the neutral Cs0. The closed circles are the data by Meth et al. [10].
3206
excitations, where three-photon resonances can appear, and also the energies of the forbidden excitations multiplied by 3/2, where two-photon resonances can appear. The peaks in the THG spectrum can be assigned as two- or three-photon resonances. We point out three properties: (1) The magnitude of X(3) at w = 0 is 1.22 x 10-12esu and is similar to the magnitudes in the THG experiments: 4 x 10-mesu at 3w -~ 1.6eV [10] and 7 x 10-nesu at 3w _~ 3.6eV [10,11]. Here, we compare the magnitudes at frequencies far from the resonances. (2) The value of the THG around the peak at 2.5eV is of the order of 10-nesu. This well explains the magnitude 2.7 x 10-1aesu at the peak centered around 2.8eV (shown by the closed circles) [10]. A larger broadening of our theory would yield better agreement with the experiment. (3) The three-photon peaks, at 3w ~ 6.1 and 6.3eV, have remarkably large strengths. This large enhancement would be due to the fact that there are two-photon resonances 3w "~ 6.1, 6.4, and 6.5eV, meaning that double resonance enhancement occurs. EXPERIMENTAL INDICATIONS The electron spin resonance (ESR) study [12] on the radical anion of C80 revealed the small g-factor, g = 1.9991, and this is associated with the residual orbital angular momentum. The irregular vibrational structure of the electronic absorption was suggested to be due to the Jahn-Teller distortion. Photoemission studies [13] of Cs0 and C70 doped with alkali metals showed appearance and shift of peak structures, which cannot be described by a simple band-filling picture. When poly(3-~dkylthiophene) is doped with C~0 [14], interband absorption of the polymer is remarkably suppressed and the new absorption peak evolves in the low energy range. The electron transfer from the polymer to C60 was proposed to be favorable in energy at account of Jahn-Teller splitting of LUMO in C~0 state and/or the Coulomb attraction of positively charged polaron to C~0. The luminescence of neutral C60 was measured [15]. There are two peaks around 1.5 and 1.7eV below the gap energy 1.9eV. The experiments were interpreted by the effect of the polaron exciton. REFERENCES 1 W. P. Su, J. R. Schrieffer~ and A. J. Heeger, Phys. Rev. B, 22 (1980) 2099. 2 K. Harigaya, J. Phys. Soc. Jpn., 60 (1991) 4001; B. Friedman, Phys. Rev. B, 45 (1992) 1454. 3 K. Harigaya, Chem. Phys. Lett., 189 (1992) 79. 4 K. tIarigaya, Phys. Rev. B, 45 (1992) 13676. 5 K. Harigaya and S. Abe, Jpn. J. AppI. Phys., 31 (1992) L887. 6 G. W. Hayden and E. J. Mele, Phys. Rev. B, 36 (1987) 5010. 7 C. S. Yannoni~ P. P. Bernier, D. S. Bethune, G. Meijer~ and J. R. Salem~ J. Am. Chem. Soc., 113 (1991) 3190. 8 A. J. Heeger, S. Kivelson, J. R. Schrieffer, and W. P. Su, Rev. Mod. Phys., 60 (1988) 781.
3207
9 C. M. Varma, J. Zaanen, and K. Raghavachari, Science, 254 (1991) 989. 10 J. S. Meth, H. Vanherzeele, and Y. Wang, preprint. 11 Z. H. Kafafi, J. R. Linde, G. S. Pong, F. J. Bartoli, L. J. Lingg, and J. Milliken, Chem. Phys. Lett., 188 (1992) 492. 12 T. Kato, T. Kodama, M. Oyam&, S. Okazaki, T. Shida, T. Nakagawa, Y. Matsui, S. Suzuki, H. Shiromaru, K. Yamauchi, and Y. Achiba, Chem. Phys. Left., 180 (1991) 446. 13 T. Takahashi, S. Suzuki, T. Morikawa, H. Katayama-Yoshida, S. ttasegawa, H. Inokuchi, K. Seki, K. Kikuchi, S. Suzuki, K. Ikemoto, and Y. Achiba, Phys. Rev. Lett., 68 (1992) 1232; C. T. Chen, L H. Tjeng, P. Rudolf, G. Meigs, L. E. Rowe, J. Chen, J. P. McCauley Jr., A. B. Smith III, A. R. McGhie, W. J. Romanow, and E. W. Hummer, Nature, 352 (1991) 603. 14 S. Morita, A. A. Zakhidov, and K. Yoshino, Solid State Cornmun., 82 (1992) 249; S. Morita, A. A. Zakhidov, T. Kawai, H. Araki, and K. Yoshino, Jpn. J. Apph Phys., 31 (1992) L890. 15 M. Matus, H. Kuzmany, and E. Sohmen, Phys. Rev. Lett., 68 (1992) 2822.
Synthetic Metals, 55-57 (1993) 3202-3207
POLARON EXCITATIONS IN DOPED C60 AND C70
Kikuo HARIGAYA Fundamental Physics Section, Electrotechnical Laboratory, Tsukuba, Ibaraki 305 (Japan)
ABSTRACT We propose a Su-Schrieffer-Heeger type electron-phonon model for fullerenes: C60 and C70. The model is solved by a numerical iteration method with applying the adiabatic approximation to phonons. When the system (C60 or C70) is doped with one or two electrons (or holes), the additional charges wccumulate along almost an equatorial line of the molecule. The dimerization becomes weaker along almost the same line. Two energy levels, the occupied state and the empty state, intrude largely in the gap. The intrusion is larger in C70 than in C60. These are "polarons" in doped fuUerenes. It is also found that C60 and C70 are related mutually with respect to electronical structures as well as lattice geometries. We also calculate optical properties of C60. In optical absorption of the doped C60, there is a new peak at lower energy than those of the intergap transition peaks. The third harmonic generation of the neutral C~0 in low frequencies agrees with experiments. Relations of polarons with recent experiments are pointed out.
INTRODUCTION AND SUMMARY Recently, the fullerenes C~ have been intensively investigated. Here, we review the recent investigation of a single C60 or C70 molecule, and discuss lattice distortion and reconstruction of electronic levels upon doping. We have described C60 and CT0 as an electron-phonon system and have extended the Su-Schrieffer-Heeger (SSH) model [1] of conjugated polymers. We have calculated for systems where one or two electrons are added or removed. We shall discuss properties of "polarons" in fullerenes, which have been reported in detail in [2-4]. We have found that sites, where additional charges are prone to accumulate, are common to C60 and CT0. They are along the equatorial line in C60. In this regard, we should bear in mind that C70 is made from C~0, by division into two parts and adding ten carbons. It is quite 0379-6779/93/$6.00
© 1993- Elsevier Sequoia. All rights reserved
3203
interesting that there are relations of electronical properties as well as the structural relation between (doped as well as undoped) Cs0 and C70. We have calculated the optical properties of C60 [4,5]. The optical transition between the HOMO and LUMO of the neutral C60 is dipole forbidden [4]. The lowest energy of the peaks of the optical absorption spectrum is about 2.9eV. When doped with additional charges, a new peak appears (at 0.7eV for electron doping and at 1.0eV for hole doping) due to the allowed transition [4]. The nonhnear optical susceptibility (third harmonic generation (THG)) of the neutral Cs0 has been calculated [5]. The magnitudes, 10 - n esu at the lowest three photon resonance and 10 -12 esu at the off resonance, agree well with experiments. We have obtained a very large peak about 10 -1° esu at 3w ,-~ 6eV owing to the double resonance enhancement. MODEL We have used the following model which is an extension of the SSH model [1] of conjugated polymers: K
2
n = ~ (-to + ~y,,,)(cLc,,. + h.c.) + 7 ~ Y'"" (,,~) (i,:),a
(1)
Here, a is the electron-phonon coupling, y,,j is the bond variable which measures the magnitude of the dimerization of the bond between the i- and j-th sites, the sum is taken from over all the nearest neighbor pairs (i,j), and K is the spring constant. This model has been applied to the geometries of Cs0 and Cr0, and solved by the adiabatic approximation. The full lattice relaxation has been realized by a numerical method shown in [4]. POLARONS IN C60 AND Cr0 We have taken to = 2.5eV, because a tight binding model with the same v~lue well reproduces the band structure of a two-dimensional graphite plane [6]. The same value has been used in polyacetylene [1]. Two quantities, c~ = 6.31eV/~
and K = 49.7eV//~ 2, have
been determined so that the length difference between the short and long bonds in C60 is the experimentally observed value: 0.05~[7]. Here, the dimensionless electron phonon coupling
~ Fig. 1. Lattice structures of doped
D
E
Cno [(a) IN¢I = 1 and (b) INcl = 2] and (c) neutral C7o
3204
A =_ 2a2/TrKto has been taken as 0.2 as in polyacetylene [1]. The number of electrons Nel has
been varied within - 2 < Nc _< 2, where Nc = N,i - N, and N is the number of carbon atoms. First, we discuss lattice and electronic structures of Cs0 [2,4]. The lattice configurations of the doped systems are shown in Fig. l(a) and (b). We show three kinds of the shorter bonds. The shortest bonds, d, are represented by the thick lines. The second shortest ones, b, are shown by the usual double lines. The dashed lines indicate the third shortest bonds. They are the bonds f in Fig. l(a) and bonds g in Fig. l(b). Other longer bonds are not shown. The figures are the same for the electron and hole dopings. When the change in the number of electrons is one, the change in the electron density is the largest at the sites at the ends of dashed lines, namely, points D. The dashed lines are mostly located along an equatorial line of C60. The absolute value of the length of the bonds g is the smallest of the four kinds of bonds with negative bond variables. The dimerization becomes the weakest along this equatorial line. The distortion of the lattice is similar to that of a polaron [8] in conjugated polymers; the spatial phase of the alternation of short and long bonds does not change upon doping, and the lattice distortion is the largest (the dimerization is the weakest) where the change in the local electron density is the largest. When the change in the electron number is two, configurations of dashed lines along the equatorial line change, as shown in Fig. l(b). The ordering of bonds, f and g, with respect to the bond variable is reversed. Other configurations are the same. The change in the electron density is also the largest at points D. Therefore, polaronic distortion persists when the doping proceeds from one to two electrons (or holes). This can be compared with a bipolaron formation in undegenerate conjugated polymers [8]. Next, we look at changes in the electronic level structures. When the system is doped, the degeneracy decreases due to the reduced symmetry. This reduction comes from the deformation of the lattice. This is one of the Jahn-Teller distortions. The removal of the degeneracies of energy levels is due to the Hg distortion [9]. When [N~[ = 1 and 2, the highest level, which splits from the HOMO of the neutral system, is undegenerate. Its energy shifts upward. In contrast, the other two leveLs shift only slightly. Similarly, the LUMO of the neutral system splits into two levels. The energy of the undegenerate level shifts downward, while change of the energy of the doubly degenerate level is small. This change in the level structures is common to two cases of the electron and hole dopings. The change is similar to that in the polaron formation [8] in conjugated polymers. We discuss changes in lattice structures and electron distributions of the doped Cr0 [3,4]. The dimerization strengths change their values mostly along the ring-like part of the molecule, while the patterns with the mirror reflection symmetry persist. Change in electron density at sites E is very small. This is a consequence of the fact that dimerization almost disappears along bonds f and g. The property of the part along the equatorial line is similar to that of the graphite plane. The strengths of the dimerization change largely along bonds, from a to e, upon doping. The additional charges tend to accumulate near these bonds. The positions D, where the additional charges accumulate most densely, correspond to the sites D of C60. When
3205
we make Cz0 from C60, sites E are added in the interval, but the property, by which additional charges tend to accumulate at sites D, persists for C70. This finding is quite interesting. We discuss structures of electronic energy levels. When the system is doped with up to two electrons or holes, the HOMO and LUMO of the neutral system largely extend into the gap. The positions of the other levels change only slightly. The magnitude of level intrusion is larger than that in C60 due to nondegenerate levels near the gap at Nc = 0. The HOMO and LUMO of the neutral system have large amplitude at sites, from A to D. The amplitude at D is the largest. The amplitude at E is very small. Therefore, the additional charge is prone to accumulate most at sites D. OPTICAL PROPERTIES We discuss how the "polarons" in C60 would be observed in optical absorption [4]. In the neutral C60, the transition between the HOMO and the LUMO (,-~ 2eV) is dipole forbidden and does not appear. In electron-doped C60, there appears a new peak at low energy (,,,0.7eV). This peak corresponds to the transition between the singly occupied molecular orbitM and the next lowest unoccupied molecular orbital, etc., when Nc = 1. It corresponds to the transition between the LUMO and the next lowest unoccupied molecular orbital, etc., when Nc = 2. Therefore, the new peak at low energy is due to the splitting of the LUMO. Similarly, the new peak appears at about leV in hole doped C60. Next, we look at spectral dispersions of the THG of the neutral C60 [5]. We display the absolute value in Fig. 2. In the bottom of the figure, we show the energies of the dipole allowed
I
0
4 i
i
III
allowed
I lil ILl '1 I I1' IIII
II
forbidden I
(eV)
I
I
I
Ill III
Fig. 2. Dispersion of third harmonic generation of the neutral Cs0. The closed circles are the data by Meth et al. [10].
3206
excitations, where three-photon resonances can appear, and also the energies of the forbidden excitations multiplied by 3/2, where two-photon resonances can appear. The peaks in the THG spectrum can be assigned as two- or three-photon resonances. We point out three properties: (1) The magnitude of X(3) at w = 0 is 1.22 x 10-12esu and is similar to the magnitudes in the THG experiments: 4 x 10-mesu at 3w -~ 1.6eV [10] and 7 x 10-nesu at 3w _~ 3.6eV [10,11]. Here, we compare the magnitudes at frequencies far from the resonances. (2) The value of the THG around the peak at 2.5eV is of the order of 10-nesu. This well explains the magnitude 2.7 x 10-1aesu at the peak centered around 2.8eV (shown by the closed circles) [10]. A larger broadening of our theory would yield better agreement with the experiment. (3) The three-photon peaks, at 3w ~ 6.1 and 6.3eV, have remarkably large strengths. This large enhancement would be due to the fact that there are two-photon resonances 3w "~ 6.1, 6.4, and 6.5eV, meaning that double resonance enhancement occurs. EXPERIMENTAL INDICATIONS The electron spin resonance (ESR) study [12] on the radical anion of C80 revealed the small g-factor, g = 1.9991, and this is associated with the residual orbital angular momentum. The irregular vibrational structure of the electronic absorption was suggested to be due to the Jahn-Teller distortion. Photoemission studies [13] of Cs0 and C70 doped with alkali metals showed appearance and shift of peak structures, which cannot be described by a simple band-filling picture. When poly(3-~dkylthiophene) is doped with C~0 [14], interband absorption of the polymer is remarkably suppressed and the new absorption peak evolves in the low energy range. The electron transfer from the polymer to C60 was proposed to be favorable in energy at account of Jahn-Teller splitting of LUMO in C~0 state and/or the Coulomb attraction of positively charged polaron to C~0. The luminescence of neutral C60 was measured [15]. There are two peaks around 1.5 and 1.7eV below the gap energy 1.9eV. The experiments were interpreted by the effect of the polaron exciton. REFERENCES 1 W. P. Su, J. R. Schrieffer~ and A. J. Heeger, Phys. Rev. B, 22 (1980) 2099. 2 K. Harigaya, J. Phys. Soc. Jpn., 60 (1991) 4001; B. Friedman, Phys. Rev. B, 45 (1992) 1454. 3 K. Harigaya, Chem. Phys. Lett., 189 (1992) 79. 4 K. tIarigaya, Phys. Rev. B, 45 (1992) 13676. 5 K. Harigaya and S. Abe, Jpn. J. AppI. Phys., 31 (1992) L887. 6 G. W. Hayden and E. J. Mele, Phys. Rev. B, 36 (1987) 5010. 7 C. S. Yannoni~ P. P. Bernier, D. S. Bethune, G. Meijer~ and J. R. Salem~ J. Am. Chem. Soc., 113 (1991) 3190. 8 A. J. Heeger, S. Kivelson, J. R. Schrieffer, and W. P. Su, Rev. Mod. Phys., 60 (1988) 781.
3207
9 C. M. Varma, J. Zaanen, and K. Raghavachari, Science, 254 (1991) 989. 10 J. S. Meth, H. Vanherzeele, and Y. Wang, preprint. 11 Z. H. Kafafi, J. R. Linde, G. S. Pong, F. J. Bartoli, L. J. Lingg, and J. Milliken, Chem. Phys. Lett., 188 (1992) 492. 12 T. Kato, T. Kodama, M. Oyam&, S. Okazaki, T. Shida, T. Nakagawa, Y. Matsui, S. Suzuki, H. Shiromaru, K. Yamauchi, and Y. Achiba, Chem. Phys. Left., 180 (1991) 446. 13 T. Takahashi, S. Suzuki, T. Morikawa, H. Katayama-Yoshida, S. ttasegawa, H. Inokuchi, K. Seki, K. Kikuchi, S. Suzuki, K. Ikemoto, and Y. Achiba, Phys. Rev. Lett., 68 (1992) 1232; C. T. Chen, L H. Tjeng, P. Rudolf, G. Meigs, L. E. Rowe, J. Chen, J. P. McCauley Jr., A. B. Smith III, A. R. McGhie, W. J. Romanow, and E. W. Hummer, Nature, 352 (1991) 603. 14 S. Morita, A. A. Zakhidov, and K. Yoshino, Solid State Cornmun., 82 (1992) 249; S. Morita, A. A. Zakhidov, T. Kawai, H. Araki, and K. Yoshino, Jpn. J. Apph Phys., 31 (1992) L890. 15 M. Matus, H. Kuzmany, and E. Sohmen, Phys. Rev. Lett., 68 (1992) 2822.