On the theory of temperature shift of the absorption curve in non-polar crystals

Antončík, E.

doi:10.1007/bf01687209

Cited by 93 publications

(50 citation statements)

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“…∇ lκµ represents the derivative with respect to the the κ-th ion position in the l-th unit cell for the µ-th direction. The shift of the band energy coming from the first order and second order derivatives are called the Fan term [61] and Debye-Waller (DW) term [62], respectively. Here, the first order modulation of the Hamiltonian can be obtained by DFPT [47].…”

Section: B Allen-heine-cardona Theorymentioning

confidence: 99%

Effect of Van Hove singularities on high- Tc superconductivity in H3S

et al. 2016

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One of interesting open questions for the high transition temperature (Tc) superconductivity in sulfur hydrides is why high pressure phases of H3S have extremely high Tc's. Recently, it has been pointed out that the presence of the van Hove singularities (vHs) around the Fermi level is crucial. However, while there have been quantitative estimates of Tc based on the Migdal-Eliashberg theory, the energy dependence of the density of states (DOS) has been neglected to simplify the Eliashberg equation. In this study, we go beyond the constant DOS approximation and explicitly consider the electronic structure over 40 eV around the Fermi level. In contrast with the previous conventional calculations, this approach with a sufficiently large number of Matsubara frequencies enables us to calculate Tc without introducing the empirical pseudo Coulomb potential. We show that while H3S has much higher Tc than H2S for which the vHs is absent, the constant DOS approximation employed so far seriously overestimates (underestimates) Tc by ∼ 60 K (∼ 10 K) for H3S (H2S). We then discuss the impact of the strong electron-phonon coupling on the electronic structure with and without the vHs and how it affects the superconductivity. Especially, we focus on (1) the feedback effect in the self-consistent calculation of the self-energy, (2) the effect of the energy shift due to the zero-point motion, and (3) the effect of the changes in the phonon frequencies due to strong anharmonicity. We show that the effect of (1)- (3) on Tc is about 10-30 K for both H3S and H2S. Eventually, Tc is estimated to be 181 K for H3S at 250 GPa and 34 K for H2S at 140 GPa, which explains the pressure dependence of Tc observed in the experiment. In addition, we evaluate the lowest order vertex correction beyond the Migdal-Eliashberg theory and discuss the validity of the Migdal approximation for sulfur hydrides.

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Section: B Allen-heine-cardona Theorymentioning

confidence: 99%

Effect of Van Hove singularities on high- Tc superconductivity in H3S

et al. 2016

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“…1 It has been theoretically identified [2][3][4] to arise from the superposition of two effects: thermal expansion of the crystal and electron-phonon interaction ͑at constant volume͒, both effects being dependent on the thermal population of the phonon modes. In this context, the measurement of a band gap ͑E G ͒ shift with temperature provides an ideal test of theories of electron-phonon interaction.…”

Section: Introductionmentioning

confidence: 99%

Effect of temperature on isotopic mass dependence of excitonic band gaps in semiconductors: ZnO

Alawadhi

Tsoi

et al. 2007

Phys. Rev. B

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The temperature dependence of the A, B, and C excitons of ZnO, observed in modulated reflectivity spectra of 68 Zn 18 O and nat Zn nat O in the range 10-400 K, reveal the superposition of band-gap renormalization originating in electron-phonon interaction and volume changes associated with thermal expansion and ͑or͒ isotopic composition in combination with anharmonicity. At low temperatures, the A, B, and C excitons in natural ZnO reach limiting values depressed from their values for the infinitely massive isotopes ͑the latter are free from electron-phonon interaction and anharmonicity͒. The C excitons of 68 Zn 18 O and nat Zn nat O converge with increasing temperature, demonstrating the independence of the band gap from isotopic mass at high temperatures.

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“…Following the early work of Fan and others in the 1950 s [5][6][7], the problem was addressed by Allen, Heine, and Cardona (AHC) [8,9], whose theory provides perturbative expressions in terms of the electron-phonon coupling; they find, at the lowest order, that two diagrams contribute to the renormalization, the Fan diagram coming from two firstorder electron-phonon coupling vertices, and the DebyeWaller diagram coming from one second-order vertex. Using semiempirical methods, and later on, density functional theory (DFT), the temperature dependence of the band gap could be obtained for several semiconductors [10][11][12][13][14][15][16][17][18].…”

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confidence: 99%

Many-Body Effects on the Zero-Point Renormalization of the Band Structure

et al. 2014

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We compute the zero-point renormalization (ZPR) of the optical band gap of diamond from many-body perturbation theory using the perturbative G0W0 approximation as well as quasiparticle self-consistent GW. The electron-phonon coupling energies are found to be more than 40% higher than standard density functional theory when many-body effects are included with the frozen-phonon calculations. A similar increase is observed for the zero-point renormalization in GaAs when G0W0 corrections are applied. We show that these many-body corrections are necessary to accurately predict the temperature dependence of the band gap. The frozen-phonon method also allows us to validate the rigid-ion approximation which is always present in density functional perturbation theory.

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On the theory of temperature shift of the absorption curve in non-polar crystals

Cited by 93 publications

References 0 publications

Effect of Van Hove singularities on high- Tc superconductivity in H3S

Effect of Van Hove singularities on high- Tc superconductivity in H3S

Effect of temperature on isotopic mass dependence of excitonic band gaps in semiconductors: ZnO

Many-Body Effects on the Zero-Point Renormalization of the Band Structure

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