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تسجيل مستخدم جديدOptical conductivity spectra of the rattling phonons and charge carriers in type-VIII clathrate Ba$_8$Ga$_{16}$Sn$_{30}$
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We have investigated optical conductivity spectra of $n$- and $p$-type Ba$_8$Ga $_{16}$Sn$_{30}$ ($alpha$-BGS) with type-VIII clathrate structure, at temperatures from 296,K down to 6,K with a terahertz time-domain spectrometer (0.2,-,2.5,THz). The continuous spectra contributed from charge carriers are dispersive in this frequency range and also temperature- and carrier type-dependent. The Drude-Smith model taking multiple-scatterings of charge carriers into account well reproduces those data. The relaxation rate of the $n$-type carriers decreases more sharply than that in the $p$-type material, suggesting that a stronger electron-phonon interaction may exist in the $n$-type than in the $p$-type. On the other hand, the localized infrared-active modes observed at 1.3,THz and 1.7,THz, identified as the rattling phonons of the Ba$^{2+}$ ions quasi-on-center vibrations, become soft and broad significantly with decreasing temperature as well as observed in type-I BGS and BGG (Ba$_8$Ga$_{16}$Ge$_{30}$) clathrates. The softening in the $n$-type is smaller by about 30% than in the $p$-type, whereas the linewidth brodening is almost the same independently on the carrier type. The difference in the softening is discussed with a scenario where the interaction of rattling phonons with carriers can modify the anharmonic potential of the guest ions. The anomalous broadening at low temepratures is also discussed by the impurity-scattering model presented for a rattling-phonon system strongly hybridized with acoustic cage phonons.
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With a terahertz time-domain spectrometer (0.3 - 3.0 THz) we have measured the optical conductivity of the type-I clathrate Ba$_8$Ga$_{16}$Sn$_{30}$ at temperatures from 300 K down to 7 K. Independent six spectra superimposed on the Drude conductivit
y are identified to infrared active vibrational modes of guest Ba ions and the cages. While the spectra of five higher-frequency modes depend hardly on temperature, the lowest-lying spectrum with a peak at 0.72 THz due to the Ba(2) ions off-centering vibration in the oversized cage changes with temperature characteristically. With lowering temperature, the spectral shape of this so-called rattling phonon continues to become so broad that the line-width amounts to be comparable to the peak frequency. Furthermore, below about 100 K, the single broad peak tends to split into two subpeaks. While this splitting can be explained by assuming a multi-well anharmonic potential, the strong enhancement of the line-width broadening toward low temperature, cannot be understood, since the Boltzmann factor generally sharpens the low-temperature spectra.
The optical conductivity spectra of the rattling phonons in the clathrate Ba$_8$Ga$_{16}$Ge$_{30}$ are investigated in detail by use of the terahertz time-domain spectroscopy. The experiment has revealed that the lowest-lying vibrational mode of a Ba
(2)$^{2+}$ ion consists of a sharp Lorentzian peak at 1.2 THz superimposed on a broad tail weighted in the lower frequency regime around 1.0 THz. With decreasing temperature, an unexpected linewidth broadening of the phonon peak is observed, together with monotonic softening of the phonon peak and the enhancement of the tail structure. These observed anomalies are discussed in terms of impurity scattering effects on the hybridized phonon system of rattling and acoustic phonons.
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The optical conductivity of charge carriers coupled to quantum phonons is studied in the framework of the one-dimensional spinless Holstein model. For one electron, variational diagonalisation yields exact results in the thermodynamic limit, whereas
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