Temperature dependence of the first-order Raman scattering by phonons in Si, Ge, and<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>α</mml:mi><mml:mo>−</mml:mo><mml:mi mathvariant="normal">S</mml:mi><mml:mi mathvariant="normal">n</mml:mi></mml:math>: Anharmonic effects

Menéndez, José; Cardona, M.

doi:10.1103/physrevb.29.2051

Cited by 761 publications

(465 citation statements)

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“…No (2) and B1g phonon modes normalized to their value at 300 K. B1g phonon exhibits an unusual softening when cooling down below 100 K. Error bars have been extracted from the Lorentzian fits. Lines are fits with a single anharmonic model 37,38 . The green dot line is a guide to the eyes.…”

Section: Resultsmentioning

confidence: 99%

“…The energy of the A 1g mode increases with decreasing temperature before saturating at 1.25% higher energy than at 300 K. It narrows upon cooling before saturating. The general temperature dependence of this mode is naturally explained by anharmonic effects 37,38 . Other ingredients, like anharmonic effect of higher rank (four-phonon process), would be necessary to accurately fit the data.…”

Section: B Sample Preparationmentioning

confidence: 99%

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Lattice dynamics of the heavy-fermion compoundURu2Si2

et al. 2015

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We report a comprehensive investigation of the lattice dynamics of URu2Si2 as a function of temperature using Raman scattering, optical conductivity and inelastic neutron scattering measurements as well as theoretical ab initio calculations. The main effects on the optical phonon modes are related to Kondo physics. The B1g (Γ3 symmetry) phonon mode slightly softens below ∼100 K, in connection with the previously reported softening of the elastic constant, C11 − C12, of the same symmetry, both observations suggesting a B1g symmetry-breaking instability in the Kondo regime. Through optical conductivity, we detect clear signatures of strong electron-phonon coupling, with temperature dependent spectral weight and Fano line shape of some phonon modes. Surprisingly, the line shapes of two phonon modes, Eu(1) and A2u(2), show opposite temperature dependencies. The A2u(2) mode loses its Fano shape below 150 K, whereas the Eu(1) mode acquires it below 100 K, in the Kondo cross-over regime. This may point out to momentum-dependent Kondo physics. By inelastic neutron scattering measurements, we have drawn the full dispersion of the phonon modes between 300 K and 2 K. No remarkable temperature dependence has been obtained including through the hidden order transition. Ab initio calculations with the spin-orbit coupling are in good agreement with the data except for a few low energy branches with propagation in the (a,b) plane.

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Section: Resultsmentioning

confidence: 99%

Section: B Sample Preparationmentioning

confidence: 99%

Lattice dynamics of the heavy-fermion compoundURu2Si2

et al. 2015

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“…3 shows the experimental results (open circles) for the line positions n(T) of one of the intralayer modes, (A H 1 4 ). The phonon frequency shift with temperature can be described by the expression [11,13,19] …”

Section: Resultsmentioning

confidence: 99%

Temperature-dependent Raman scattering spectra of ε-GaSe layered crystal

Gasanly

Aydınlı

Özkan

et al. 2002

Materials Research Bulletin

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The temperature dependencies (15±300 K) of seven Raman-active mode frequencies and linewidths in layered gallium selenide have been measured in the frequency range from 10 to 320 cm À1 . We observed softening and broadening of the optical phonon lines with increasing temperature. Comparison between the experimental data and theories of the shift and broadening of the intralayer phonon lines during heating of the crystal showed that the experimental dependencies can be explained by the contributions from thermal expansion, lattice anharmonicity and crystal disorder. The pure-temperature contribution (phonon± phonon coupling) is due to three-phonon processes. Moreover, it was established that the effect of crystal disorder on the linewidth broadening of TO mode is stronger than that of LO mode. #

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“…[19,20,21] Besides, the temperature dependence of the phonon frequency and linewidth measured by Raman scattering can give some insight about the anharmonicity of the E 2g mode. In general, due to the lattice expansion contribution, [22] the harmonic phonon frequency is temperature-dependent and in the lowest order is given by:…”

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Role of the E2g phonon in the superconductivity of MgB2: a Raman scattering study

Martinho

Rettori

Pagliuso

et al. 2003

Solid State Communications

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Temperature-dependent Raman scattering studies in polycrystalline MgB2 (10 < T < 300 K) reveal that the E2g phonon does not experience any self-energy renormalization effect across the superconducting critical temperature TC ≈ 39 K, in contrast with most of the current theoretical models. In the presence of our results, those models must be reviewed. The analysis of the temperature dependence of the E2g phonon frequency yields an isobaric Grüneisen parameter of | γE 2g | 1, smaller than the value of 3.9 obtained from isothermal Raman experiments under pressure. It is suggested that this apparent disagreement can be explained in terms of pressureinduced changes of the topology of the Fermi surface. MgB 2 has attracted much recent interest due to its remarkable physical properties such as: i) relatively high superconducting transition, T C = 39 K, for a binary compound with a simple crystal structure, ii) large and anisotropic coherence lengths, critical fields and current densities, and iii) critical currents that are not limited by grain boundaries (absence of weak link effects). [1] MgB 2 forms in a hexagonal structure with space group P6/mmm (D 1 6h ). The B atoms are located on a primitive honeycomb lattice consisting of graphite-type sheets. The B 2 -layers are intercalated with Mg-layers that also form a honeycomb lattice with a Mg atom in the center. For this space group, factor-group analysis predicts four modes at the Γ point: E u + A 2u + E 2g + B 1g , where only the E 2g mode is Raman-active and the B 1g mode is silent. The E 2g phonon is a doubly degenerate in-plane B-B bond-stretching mode[2] with nonvanishing Raman tensor elements (α xx − α yy ) and α xy . First principles lattice dynamics calculations indicate that these modes would be observed at 327 cm −1 (E u ), 405 cm −1 (A 2u ), 572 cm −1 (E 2g ) and 702 cm −1 (B 1g ). [3] In analogy with high T C superconductors (HTS), Hall effect measurements [4] indicate that the charge carriers in MgB 2 are holes with a hole density at 300 K of 1.7 − 2.8×10 23 holes/cm 3 . In fact, hole-mediated su- * Electronic address: hercules@ifi.unicamp.br; URL: http://www.ifi.unicamp.br/gpoms perconductivity has been proposed by An and Pickett for MgB 2 .[5] These authors attribute the relatively high value of T C to the strong coupling between holes and the in-plane boron phonon, E 2g modes. According to this model, the holes originate in the σ (sp 2 orbitals) bands due to charge transfer from the σ bands to the π (p z orbitals) bands. Based on this model, several papers have discussed the possibility of E 2g phonon being a frozen-in mode, strongly coupled to the σ electronic bands near the Fermi level. [2,3,6,7] It is claimed that the E 2g phonon, due to its rather strong coupling to the σ electronic bands, would be highly anharmonic, presenting a very large linewidth. However, Boeri et al [8] pointed out that neither the presence at the Fermi level of the σ bands nor their strong coupling to the E 2g phonon are sufficient to induce such anharmonic effects, and the...

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Temperature dependence of the first-order Raman scattering by phonons in Si, Ge, andα−Sn: Anharmonic effects

Cited by 761 publications

References 27 publications

Lattice dynamics of the heavy-fermion compoundURu2Si2

Lattice dynamics of the heavy-fermion compoundURu2Si2

Temperature-dependent Raman scattering spectra of ε-GaSe layered crystal

Role of the E2g phonon in the superconductivity of MgB2: a Raman scattering study

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