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EFFECT OF ELECTRON-PHONON INTERACTION ON RAMAN SPECTRA OF GRAPHITE
INTERCALATION COMPOUNDS
H. Miyazaki, C. Horie
To cite this version:
H. Miyazaki, C. Horie. EFFECT OF ELECTRON-PHONON INTERACTION ON RAMAN SPEC- TRA OF GRAPHITE INTERCALATION COMPOUNDS. Journal de Physique Colloques, 1981, 42 (C6), pp.C6-335-C6-337. �10.1051/jphyscol:1981698�. �jpa-00221635�
JOURNAL DE PHYSIQUE
CoZZoque C6, suppZ6ment a u n o 12, Tome 42, d6cembre 1981 page c6-33s
EFFECT OF ELECTRON-PHONON INTERACTION ON RAMAN SPECTRA OF GRAPHITE INTERCALATION COMPOUNDS
H. Miyazaki and C. Horie
Department o f A p p l i e d P h y s i c s , Tohoku U n i v e r s i t y , S e n d a i , Japan.
Abstract.-Theoretical study is presented of effects of electron=
phonon interactions on Raman spectra of acceptor graphite inter- calation compounds of stages 3 and 4. It is discussed that the spectral shape of the doublet peaks observed at around 1600 cm-1 is practically Lorentzian contrary to the case of stage 1
compounds intercalated with alkali metals. It is also shown that the coupling of Raman-active phonons with electrons local- ized mostly on carbon layers adjacent to intercalants yields the doublet separation of about 10 cm-1.
1. Introduction.- Even though there are a large amount of experimental studies of the lattice dynamics of graphite intercalation compounds
(GIC), only few theoretical studies have been carried out for phonon properties mainly because of complexity of the system. In the previous paper [l], we have shown that the dynamical coupling between electron and Raman-active phonon plays an essential role in determining the anomalous line shape of Raman spectra near 1500cm-~ of the first stage GIC intercalated with alkali metals. The same idea is extended to higher stage GIC, in which the electronic structure is different from the first stage GIC. Our main emphasis is to show that the dynamical effect of the electron-phonon coupling still plays an important role in determining the doublet structure of Raman spectra observed near 1600cm-~ of GIC's with stage n 2 3. In the present paper, we focus our attention to the case of acceptor compounds of stages 3 and 4 because of simplicity of calculations. Our results show that about one half of the magnitude of the doublet separation in the Raman spectra ob- served is attributed to the difference in electron-phonon couplings;
one with electrons localized on carbon layers adjacent to intercalants and the other with electrons distributed on interior carbon layers. It is argued that the spectral line shape is practically Lorentzian con- trary to the case of the first staqe GIC intercalated with alkali metals.
2. Model.- It has been established that the lower frequency component
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1981698
C6-336 JOURNAL DE PHYSIQUE
of the doublet of Raman spectra for acceptor GIC's is attributed to
E O modes of interior graphite layers, whereas the upper component
2'32
is associated with
s2
modes of bounding graphite layers adjacent to intercalants [2]. Our main interest is to study how electron-phonon 92 coupling contributes to the large up-shift of the 6 mode relative to the E0 mode, which is observed to be about 20 cm-l for all 292-2
acceptor GIC's studied. For this purpose we start with an electronic band structure of stages 3 and4 acceptor GIC's calculated by Blinowski and Rigaux [3]. In their model, the electronic charge distribution on carbon layers adjacent to an intercalant layer and the corresponding band structure are calculated self-consistently for a given charge transfer f, which is defined by a fraction of charge transfer per one intercalant. The band structure determined, then, is adopted to cal- culate self-energies of electrons by taking into account the inter- action with both longitudinal and transverse acoustic phonons, because these phonons have a comparable magnitude of coupling with electrons
[4]. The Raman-active phonon self-energies due to the coupling with the renormalized electrons are, then, calculated by solving the Dyson equation self-consistently. In accordance with the model described above, the phonon associated with the bounding $ mode interacts pri-
292
marily with electrons mostly localized on the carbon layer adjacent to intercalant layer, whereas the phonon associated with interior E0 mode interacts primarily with electrons residing on interior carbon 2g2 layers. Since the charge distribution along the c-axis is found to be strongly localized on the carbon layers adjacent to an intercalant layer, the renormalized phonon frequency determined is found to be different for 2 and E O modes, respectively. The phonon frequency
2g2 2P2
difference A f l is listed In TableIfor several values of charge trans- fer f. The coupling constant of electron with Raman-active phonons was taken to be O.leV 111. Since the renormalized phonon frequencies fall in or are close to electronic excitation energies, the most important contribution to the Raman scattering cross-section is given by oiC) (see eq. (7) in [I] ) , which might give rise to a Fano-type resonance when the Fano parameter Q is close to
+
1. In fact, theis written as
where n indicates a number of bounding or interior layers, Ro is the j
E mode frequency, E = (Aw
-
Rj)/Tj, and the sum is taken over2g2 j
bounding and interior modes. Contributions other than ojC) are found to yield a broad and almost flat background. In Table I are listed
the Fano parameter Q and the I' for each mode. The value of r is
determined by the imaginary part of the phonon self-energy and gives a measure of the Raman line width.
Table I : Frequency shift As2=QB-S2= and line shape parameter, Q and r, as a function of charge transfer f. Suffices B and I indicate bounding and interior modes, respectively.
3. Conclusion.- The present calculation of Raman spectra has been carried out at zero temperature. It has been found that the Fano parameters calculated are far from unity and the line shape of both
6 and E O peaks are practically Lorentzian. We can also conclude
2g2 2g2
that the dynamical effect of electron-phonon coupling yields the doublet separation of about one half of the magnitude observed in Raman spectra of stages 3 and 4 acceptor GIC1s. The remaining shift between 6 and E O can be attributed to the difference in ion-ion
2g2 2"2
interactions [51. It 1s also noticed that a slight increase of AR with increasing f is due to the increase in the localized charge distribu- tion on the bounding layers adjacent to the intercalant layer. It is clear then that the doublet separation would be strongly linked with the value of charge transfer, though the value of f is not definitely known at present for all acceptor GIC1s of stages 3 and 4 studied.
References.
[l] Miyazaki H., Hatano T., Kusunoki G., Watanabe T., and Horie C., Physica 105B (1981) 381.
[2] u n d e r h i l l , Leung S.Y., Dresselhaus G., and Dresselhaus M.S., Solid State Commun. 29 (1979) 769.
[3] Blinowski J. and ~ i g a u x C., J. Physique 41 (1980) 667.
[4] Pietronero L. and ~tr3ssler S., Proc. 1.5th Int. Conf. Physics of Semiconductors, Kyoto (1980) 895.
[51 Dresselhaus M.S. and Dresselhaus G., Adv. Phys. 30 (1981) 139.
