Electron-phonon interaction in tetrahedral semiconductors

Considerable progress has been made in recent years in the field of ab initio calculations of electronic band structures of semiconductors and insulators. The one-electron states (and the concomitant two-particle excitations) have been obtained without adjustable parameters, with a high degree of reliability. Also, more recently, the electron-hole excitation frequencies responsible for optical spectra have been calculated. These calculations, however, are performed with the constituent atoms fixed in their crystallographic positions and thus neglect the effects of the lattice vibrations (i.e. electron-phonon interaction) which can be rather large, even larger than the error bars assumed for ab initio calculations.Effects of electron-phonon interactions on the band structure can be experimentally investigated in detail by measuring the temperature dependence of energy gaps or critical points (van Hove singularities) of the optical excitation spectra. These studies have been complemented in recent years by observing the dependence of such spectra on isotopic mass whenever different stable isotopes of a given atom are available at affordable prices. In crystals composed of different atoms, the effect of the vibration of each separate atom can thus be investigated by isotopic substitution. Because of the zero-point vibrations, such effects are present even at zero temperature (T=0).In this paper, we discuss state-of-the-art calculations of the dielectric function spectra and compare them with experimental results, with emphasis on the differences introduced by the electron-phonon interaction. The temperature dependence of various optical parameters will be described by means of one or two (in a few cases three) Einstein oscillators, except at the lowest temperatures where the T⁴ law (contrary to the Varshni T² result) will be shown to apply. Increasing an isotopic mass increases the energy gaps, except in the case of monovalent Cu (e.g. CuCl) and possibly Ag (e.g. AgGaS₂). It will be shown that the gaps of tetrahedral materials containing an element of the first row of the periodic table (C,N,O) are strongly affected by the electron-phonon interaction. It will be conjectured that this effect is related to the superconductivity recently observed in heavily boron-doped carbon.     

Effective electron Hamiltonian for a quasi one-dimensional system. The (TMTSF)2X and the (TMTTF)2X systems

In this paper we have introduced a variational approach to investigate the ground state of a model which includes both the Holstein electron-phonon interaction and the extended Hubbard electron-electron interaction. We have considered a variational state for the phonon subsystem which generalizes the previous used forms. This state allows to take into account the possibility of extended phonon mediated correlations. The effective electron Hamiltonian, which we have obtained, includes first and second neighbor electron-electron interaction terms. We have treated exactly, through a Lanczos method, this effective model in the one-dimensional case. We have applied our method to two Bechgaard salts and in these cases we have estimated the correlation parameters. We have shown that the introduction of electron-phonon interaction allows an estimate of the on site U and nearest-neighbor V Coulomb repulsion, which are in agreement with the experimental optical spectra of the above mentioned two compounds. Received: 30 October 1997 / Revised: 28 January 1998 / Accepted: 10 April 1998     

Interband transitions and electronic Raman continuum in systems with strong inelastic scattering: Applications to YBa2Cu3O7-δ

We consider a model for the electronic Raman continuum which takes into account strong inelastic scattering and interband transitions. Calculations are based on four-vertex Raman scattering diagrams (Kawabata formalism) within the RPA for Coulomb interaction and the ladder diagram Bethe-Salpeter equation for the vertex. We apply this method to an analysis of the nature of the electronic Raman continuum in the normal state of the high-T _c superconductor YBa₂Cu₃O₇. In numerical calculations we take into account all the self-energy effects and make simulations for vertex corrections assuming that inelastic scattering is due to electron-phonon interaction. Theab-plane polarized continuum contains a large contribution from interband processes and does not depend strongly on temperature and inelastic scattering strength. The in-plane anisotropy is determined by interband transitions rather than by anisotropy of the Fermi surface. The ZZ continuum contains only weak contribution from interband transitions. It can be crudely described within a single band model with inelastic scattering and is strongly dependent on the relaxation rates of inelastic scattering. The nature of the oxygen-deficiency dependence of the Raman spectra is also commented upon.     

Second order resonant Raman scattering at the E1 and E1 + Δ1 edges of germanium

The resonance of the 2TO phonon second order Raman band of germanium was investigated in the vicinity of the E₁, E₁ + Δ₁ gaps. The peak reported earlier for 2TO phonons at Γ is interpreted as due to a resonant process of the iterative type, involving two first order electron-phonon vertices. The rest of the 2TO band is interpreted as a process involving a second order electron-two phonon interaction vertex. From these measurements three phonon coupling constants for the electron-two phonon interaction are obtained.     

-wave nonadiabatic superconductivity

The inclusion of nonadiabatic corrections to the electron-phonon interaction leads to a strong momentum dependence in the generalized Eliashberg equations beyond Migdal's limit. For a s-wave symmetry of the order parameter, this induced momentum dependence leads to an enhancement of when small momentum transfer is dominant. Here we study how the d-wave symmetry affects the above behavior. We find that the nonadiabatic corrections depend only weakly on the symmetry of the order parameter provided that only small momentum scatterings are allowed for the electron-phonon interaction. In this situation, We show that also for a d-wave symmetry of the order parameter, the nonadiabatic corrections enhance . We also discuss the possible interplay and crossover between s- and d-wave depending on the material's parameters. Received 12 May 2000     

Cusp satellite bands in the spectrum of molecule

We report measurements and a theoretical explanation of the cusp-shaped satellite bands in the blue wing of the cesium D₂ resonance line which have been observed for the first time. The bands are identified as transitions where the upper state dissociates into the 6 ²P _3/2 + 6 ² S _1/2 atomic asymptote. The experiment has been performed using a standard absorption setup, computer controlled data acquisition and computer data processing. We have shown that the peculiar shape of the difference-potential curve is solely responsible for the spectrum containing the cusp-shaped satellite bands. The appearance of these satellite bands has been discussed and explained relating the theory of satellite bands to the catastrophe theory. The shape of the line wing and of the satellite bands have been calculated using the Fourier transform technique. To ensure a more stringent comparison between the experimental and the theoretical spectrum, we have analyzed and compared the derivatives of the measured and the calculated satellite band shape. On the contrary to the customary direct comparison between the measured and the calculated absorption coefficient, the derivative clearly shows all differences and resemblances between satellite band profiles. The degree of coincidence of the experimentally observed and the theoretically calculated satellite band shape can be used as an ultimate check on the assessment of the quality of potential-energy curves involved in the formation of satellite bands. Received: 1 October 1997 / Revised: 14 January 1998 / Accepted: 24 February 1998     

Ab initio calculations of the electron-phonon interaction and characteristics of large polarons in rutile and anatase

The calculations of the electron-phonon interaction and some characteristics of excited electrons near the bottom of the conduction band of titanium dioxide in the structure of anatase and rutile have been performed. The Eliashberg function, the imaginary and real parts of the self-energy potential, as well as the band and polaron masses and width of the photoemission line, have been calculated. It has been shown that the electron-phonon interaction is primarily determined by the interaction with optical photons. Moderate values of the polaron mass (<2m _e ) correspond to large polarons. The calculated values of the spectral line width are significantly less than those observed in the experiment. Arguments have been presented in support of the assumption that the main contribution to the spectral line width corresponds to the interaction of electrons with the potential of randomly arranged oxygen vacancies.     

Temperature dependence of the fundamental energy gap in GaAs

We show that the temperature dependence of the fundamental gap energy E₀ of GaAs can be theoretically described within the empirical local pseudopotential approach for the band structure. For the calculation we take into account the thermal expansion effect and two contributions of the deformation potential type electron-phonon interaction. These are the Debye-Waller part, which shifts the gap to lower energies with increasing temperature, and the self-energy part, which partly cancels the shift caused by the Debye-Waller part.     

Pressure dependence study on the electron-phonon coupling of thulium hexachloroelpasolite

Raman spectra of Cs₂NaTmCl₆ have been recorded using a diamond anvil cell at ambient temperature. The vibrational energy of each of the Raman-active TmCl₆⁻³ moiety modes increases linearly with pressure. The integrated band areas of the ν₁(a_1g) and ν₂(e_g) modes are independent of applied pressure. However, the band area of the ν₅(t_2g) mode shows an anomalous behaviour, which has been qualitatively interpreted as due to electron-phonon coupling of the aΓ₅ electronic state with the Γ₁+ν₅(t_2g) vibronic state. This interaction between the coupled states is strongest between ca. 10 and 13 GPa at ambient temperature. The results serve to emphasize the specificity of the occurrence of strong electron-phonon coupling for particular transitions of a given rare earth ion.     

Electronic structure and structural phase stability of CuAlX2 (X=S, Se, Te) under pressure

The electronic and structural properties of chalcopyrite compounds CuAlX₂ (X=S, Se, Te) have been studied using the first principle self-consistent Tight Binding Linear Muffin-Tin Orbital (TBLMTO) method within the local density approximation. The present study deals with the ground state properties, structural phase transition, equations of state and pressure dependence of band gap of CuAlX₂ (S, Se, Te) compounds.Electronic structure and hence total energies of these compounds have been computed as a function of reduced volume. The calculated lattice parameters are in good agreement with the available experimental results. At high pressures, structural phase transition from bct structure (chalcopyrite) to cubic structure (rock salt) is observed. The pressure induced structural phase transitions for CuAlS₂, CuAlSe₂, and CuAlTe₂ are observed at 18.01, 14.4 and 8.29 GPa, respectively. Band structures at normal as well as for high-pressure phases have been calculated. The energy band gaps for the above compounds have been calculated as a function of pressure, which indicates the metallic character of these compounds at high-pressure fcc phase. There is a large downshift in band gaps due to hybridatization of the noble-metal d levels with p levels of the other atoms.     

Infrared band contour analysis and molecular constants of SPF3 and NSF3

Infrared spectra of gaseous SPF₃ and NSF₃ have been recorded at various temperatures. The band contours of the E fundamentals were analyzed by computer simulation taking into account the dependence of the rotational constants on the vibrational state. The ζ values together with centrifugal distortion constants (only for SPF₃) and isotope shifts Δν_i(³²S/³⁴S) were used as additional data in force constant calculations. CNDO calculations have been carried out to distinguish between two sets of force constants for the E block of NSF₃. An interpretation of the calculated stretch-stretch interaction force constants, f_rR, is given. Anharmonicity constants X₄₆ for SPF₃ and NSF₃ were determined.     

Isotope shifts and hyperfine structure in the transitions in calcium II

The isotope shift and hyperfine structure in the three - transitions in Ca II have been studied by fast ion beam collinear laser spectroscopy for all stable Ca isotopes. The metastable 3d states were populated within the surface ionization source of a mass separator with a probability of about 0.1%. After resonant excitation to the 4p levels with diode laser light around 850 nm the uv photons from the transitions to the ground state were used for detection. Hyperfine structure parameters A and B for the odd isotope ⁴³Ca, as evaluated from the splittings observed, agree well with theoretical predictions from relativistic many-body perturbation theory. Field shift constants and specific mass shift constants were extracted from the measured isotope shifts and are discussed in comparison with expectation values from theory. Received: 19 September 1997 / Revised: 5 December 1997 / Accepted: 27 January 1998     

Constraints on the mechanism of superconductivity for MgB2 from Tc and the total isotope effect

We examine the possible electron-phonon spectra that produce both T_c=39 K and an isotope coefficient β=0.32±0.01, with Eliashberg theory. We assess the viability of the conventional electron-phonon mechanism in light of these results, compared with ab initio calculations of the electron-phonon spectrum. Comparisons are made with similar considerations for low T_c materials.     

Brillouin scattering study of transverse elastic waves in the α, incommensurate and β phases of AlPO4

Transverse and pseudo-transverse elastic waves have been studied in several scattering geometries in order to investigate the temperature dependences of C E ₆₆ and C E ₁₄ over the range 300-1100 K, including the transitions near 860 K. These results complete those on C E ₄₄ we have obtained in a previous work. All these constants display discontinuities at the lock-in transition. In the phase, the results are analysed in term of lowest order couplings between strains (e) and the order parameter (Q). The main features are described by the lowest order biquadratic e2Q2 coupling, in particular for C E ₄₄ in a large temperature range. However, it appears that a contribution of the next coupling term arises for C E ₆₆ below K and that the first two lowest order terms have to be taken into account even just below the lock-in transition in the case of C E ₁₄ . The temperature dependence of Q has been deduced and it can be well described in the framework of Landau's theory. Received: 2 October 1997 / Received in final form: 3 December 1997 / Accepted: 29 January 1998     

Isotopic shift in angle-resolved photoemission spectra of Bi2Sr2CaCu2O8 due to quadratic electron-phonon coupling

In connection with the experiment on oxygen isotope effect of Bi₂Sr₂CaCu₂O₈ with the angle-resolved photoemission spectroscopy (ARPES), we theoretically study the isotope-induced band shift in ARPES by the Hartree-Fork and quantum Monte Carlo methods. We find that this band shift can be clarified based on a quadratically coupled electron-phonon (e-ph) model. The large ratio of band shift versus phonon energy change is connected with the softening effect of phonon, and the positive-negative sign change is due to the momentum dependence of the e-ph coupling.     

The band structure and optical properties of the CdxHg1-xTe mixed crystals

The band structure of the Cd_xHg_1?xTe mixed crystals have been computed on the basis of tight-binding interpolation scheme and virtual crystal approximation. The bowing parameters of main energy gaps have been calculated as well as composition dependence of position of E₁ and E₁ + Δ₁ maxima in reflectivity spectra. Good agreement with previously reported experimental data has been found.     

Ab initio calculation of optical absorption and reflectivity of Si(0 0 1)/SiO2 superlattices with varying interfaces

Using first-principles calculations we investigate the influence of interface modification and layer thicknesses on the optical properties of Si/SiO₂ superlattices. Four interface models with different dangling-bond passivation are considered. The results demonstrate confinement effects not only for the fundamental band gaps but also for the optical properties. While for a large Si layer thickness of the Si/SiO₂ superlattices the interface dependence is small, the calculations show a significant structure dependence for thin Si layers. © 2007 Elsevier Science. All rights reserved.     

稀掺杂GaNxAs1－x(x≤0.03)薄膜的调制光谱研究

利用室温下压电调制反射光(PzR)谱技术系统测量了N掺杂浓度为0.0%—3%的分子束外延生长GaN_xAs_1-x薄膜，并对图谱中所观察的光学跃迁进行了指认.在GaN_0.005As_0.995和GaN_0.01As_0.99薄膜的PzR谱中观察到此前只在椭圆偏振谱中才看到的N掺杂相关能态E₁+Δ₁+Δ_N.当N掺杂浓度达到 关键词： 压电调制反射光谱(PzR) xAs_1-x薄膜')" href="#">GaN_xAs_1-x薄膜 分子束外延(MBE)     

Optical studies of (NH4)2SO4 single crystal in the paraelectric phase

Transmittance and absorbance spectra of (NH₄)₂SO₄ single crystals along [010] direction were measured at different temperatures (296, 308, 318, 328 and 348 K) in the paraelectric phase. The absorption coefficient was computed and the analysis of the data revealed the existence of two optical transitions in (NH₄)₂SO₄ single crystals. The direct and indirect band gaps were shifted towards the longer wavelength with increasing temperature. The data on the allowed indirect transition was analyzed and interpreted in terms of two valence bands originated by spin orbit interaction and crystal field splitting. The momenta E_p were calculated as the difference between E_g1, the first valence to conduction band, and E_g2 for the second valence band at different temperatures. The results of extinction coefficient (k), the refractive index (n), and dielectric constants (ε) were also discussed and calculated as a function of wave length (λ). The heat treatment of the crystals proved that the variations of these optical parameters can be consequence of the internal microstructure changes caused by annealing.     

新型超导体MgB2的热电势和电阻率研究

测量了MgB₂的热电势和电阻率与温度的依赖关系.在100K—300K区间,热电势呈近似线性温度依赖关系,其斜率为正,表明载流子为空穴型且与能带贡献的图像相一致.与此对应,在此温区电阻率呈T²依赖关系.在100K以下,热电势和电阻率各自转变了其高温区的温度依赖关系.热电势在超导转变温度T_c(零电阻366K)到100K间有一宽峰,具有声子曳引峰的特征,表明电子-声子相互作用很强.估算了一些重要的参数,如带米能E_F、能带宽度 关键词： 新型超导体 热电势 电阻率