We shall consider two important mechanisms for the decay of long-wavelength acoustic phonons in single-wall CNTs, namely electron-phonon (e-ph) and ph-ph scatter- ing. We show that the dominant e-ph coupling terms (re- sulting from the deformation potential contribution) do not allow for phonon decay due to kinematic restrictions, and thus an intrinsic upper bound for the temperature- dependent quality factor of the various modes can be derived from ph-ph interactions alone. These upper bounds are given below. The problem of phonon de- cay has in fact a rather long history. Early work on the decay of an optical phonon into two acoustic phonons via anharmonicities 45,46 proposed a scheme for nonlin- ear phonon generation. Phonon decay via ph-ph inter- action is also important for the understanding of neu- tron scattering data 40 and for the collective excitations in liquid helium. 47 Such effects have even been consid- ered in a proposal for a phonon-based detector of dark matter. 48 General kinematic restrictions often prevent the decay of phonon modes. Lax et al. have shown 49 that a given acoustic phonon cannot decay into other modes with higher velocity at any order in the anharmonicity.
This paper is organized as follows. In Section II, the DC and 3DP models for lattice- matched InAlN/AlN/GaN heterostructures are described where the polar phonon modes and associated electron-phononinteractions are given. Then in Section III a formulation of the power dissipation and energy relaxation time in such heterostructures is presented, taking into account non-equilibrium polar optical phonons, electron degeneracy, and screening from the mobile electrons. Effective numerical techniques in calculating the generation rates and power loss are also described, in terms of handling the integrals involved. In Section IV, first we show results of the non-equilibrium phonon occupation numbers for both half-space and interface modes in a typical lattice-matched InAlN/AlN/GaN heterostructure. These results are used to analyze how hot phonons slow down the quasi-2D electron energy relaxation in the high-temperature region. Then, by choosing two GaN heterostructures with different channel widths we compare power dissipation results from the DC and 3DP models for the simple case with no screening. This is to check the sum rules as well as investigate phonon confinement effects and roles the half-space and interface modes play in the respective pure and net phonon emission processes. In order to examine the usual 3DP approximation in the evaluation of energy relaxation, we further compare the DC and 3DP results of power loss and energy relaxation time in the lattice-matched heterostructure for a number of detailed phonon scattering processes with or without electron screening. Comparisons with the experimental data as well as the bulk GaN situation are also made, and the hot-phonon and screening effects are discussed in great detail. Finally, Section V summarizes the main results obtained. In Appendix A, starting with the detailed generation rate expressions for the half- space, interface and bulk LO phonons, a restoration of the Mori-Ando sum rule is made.
using second-order force constants, and hence shown the enhanced anharmonicity to be an inherent property of this system. This scheme may form a practical basis for studying other important classes of system with displacive instabilities, e.g., halide perovskites. From a materials- design perspective, similar anharmonic phonon dampening may occur in other systems at the boundary of a phase transition, and so this could serve as a selection criterion for identifying materials with ultralow thermal conductivity . In these materials, the poor thermal transport is a bulk property, and so the potential negative impact on electrical properties of modifications such as doping and nanostruc- turing may be avoided. Understanding this phenomenon may thus provide a robust design strategy for developing thermal insulators and high-performance thermoelectric materials.
FIG. 3. Effective mass and quasiparticle residue in the SrTiO 3 2DEL. Evolution of the effective mass m ∗ (blue symbols) and quasiparticle residue Z (red symbols) with carrier density.
Different symbols indicate data taken on substrates annealed at different temperature. Closed red symbols are obtained from Franck-Condon fits, while the last value with open symbol in the adiabatic Migdal-Eliashberg regime has been calculated from Z = m 0 /m ∗ . Error bars indicate the reproducibility of our results. An additional systematic error cannot be excluded. The background color encodes the bare band width of the first light subband calculated from the experimentally determined k F shown in the top-axis, assuming a bare mass of m 0 = 0.6 m e . Dashed lines are guides to the eye. The dome shaped superconducting phase observed at the LaAlO 3 /SrTiO 3 interface is indicated in grey.
Again with the lowering of lattice temperature a number of features arises which are different from those of higher lattice temperatures. To mention in particular, the effect of finite phonon energy on electron-phononinteractions, the non-equipartition energy distribution of phonons, the degeneracy of the free carrier ensemble, the electrostatic screening of the scattering potential by the electrons are dominant factors of electron-phonon scattering at low lattice temperatures. Taking all these features into account at a time it is very difficult to study the electrical transport in 2DEG and to perform the same one adopts theoretical models imparting reasonable approximations in respect of lattice temperature and carrier concentration. Some works on the study of electrical transport in 2DEG at low temperatures have already been reported by the present author [10, 13-17].
4 Thermoelectricity in semiconductors is the response of electron and phonon currents to temperature gradients. The interaction between the electrons and phonons plays a crucial role in this response. To maximize the thermoelectric response, one needs to selectively heat electrons and minimize the electron-phonon interaction to avoid heat leakage to the lattice. Only the energy delivered by the electrons is the conversion of heat to electrical energy, the part delivered by phonons is wasted. In practice, phonons always exist at finite temperatures and take some of the input heat directly from the source and some through electron-phonon energy exchange. Both, lower the performance and serve as heat leaks. Electron-phonon interaction is an important phenomenon in condensed matter physics beyond thermoelectricity. Many experimental observations such as temperature-dependent band structures, zero-point renormalization of the bandgap in semiconductors, conventional phonon-mediated superconductivity, phonon-assisted light absorption, Peierls instability , the Kohn effect , temperature-dependent electrical resistivity as well as traditional superconductivity  are caused by the electron-phonon interaction. The role of electron-phononinteractions in the transport properties of systems with strong electron-phonon correlations is one of the central issues in the theory of strongly correlated systems.
The advanced Si technology has prompted most of the studies in semiconductor physics. Along with these studies a considerable number of works have also been initiated on III-V and II-VI compound semiconductors. Gallium Arsenide, one of the III-V-compound semiconductors has attracted considerable interest for application in semiconductor heterostructures and nanostructures because of its highelectron mobility. It finds use in many devices like tunnel diodes, Gunn effect devices, lasers, etc. Thus a good number of theoretical studies on the conductivity characteristics have been reported starting from a rather low temperature to high temperatures both in bulk semiconductors as well as in two-dimensional electron gas formed in semiconductor surface layers [1-10,]. In these analyses, a detailed physical formulation of various scattering mechanisms like ionized impurity scattering, acoustic phonon scattering, piezoelectric scattering, polar and non-polar optical phonon scatterings, carrier–carrier scattering, and alloy scattering has been made to accurately determine the variation of mobility with carrier concentration and temperature.
Germanium has diamond type structure. It has two identical atoms in primitive unit cell. An equation of motion technique of quantum dynamics has been applied to develop the theory of Raman spectra of germanium. An expression for electronphonon linewidth and electronphonon shift has been obtained. It is established fact that at hightemperature limit when anharmonic effects are dominant, the contributions of harmonic field, localized field, electronelectron interaction field are feeble. It has been found that at hightemperature limit, cubic and quartic parts of electronphonon linewidth and electronphonon shift have been matched with the Balkanski et al. model for linewidh and shift at hightemperature. An analysis of first order Raman spectra of germanium has been carried out on taking anharmonicity upto quartic terms.
Abstract:- An equation of motion technique of quantum dynamics and Dyson equation approach have been used to obtain Fourier transformed electron Green`s function in presence of isotopic impurity and anharmonicity Hamiltonian has been taken as a sum of harmonic part , electron part , defect part , electronphonon interaction part , anharmonic part .The anharmonicity has been taken upto quartic terms . The response function has been obtained responsible for electronphonon linewidth . At hightemperature, an expression of electron density of states (EDOS) has been obtained according to different fields present in semiconductor continuum. An EDOS has also been influenced by perturbed mode energy .The effect on intensity of peaks with respect to temperature and different excitations has been undertaken in this framework.
The purpose of the following chapter was to provide the reader with a detailed description of the problem. First, we have explicitly derived basic correlation functions, including two- point Green functions for translation invariant system. We have introduced a Luttinger parameter K, which describes the effective strength of electron-electroninteractions, and v, the velocity of plasmonic excitations in the system. This was followed by the discussion of the problem of a single impurity embedded in a Luttinger Liquid. We have outlined the main results obtained in Refs.  and  and, thereby, built a foundation for our main calculations. We have proved the duality relation between the weak and strong impurity limits in the Luttinger Liquid. Also in this chapter, with the help of functional bosonisation, we have developed the description of a Luttinger Liquid coupled to one-dimensional acoustic modes. The presence of phonons strongly modifies the system and results in a Luttinger Liquid two polaronic modes, slow and fast, with the velocities determined by the strength of electron-electron and electron-phononinteractions. One also discovers an intrinsic instability of a system at high values of electron-phonon coupling, called Wentzel-Bardeen instability.
The high temperatures that develop in the proximity of the gold layer are potentially attractive for enhancing the rate of several chemical reactions 9 . In this work we take advantage of these high temperatures to drive photothermochemical transformations for the conversion of ethanol to generate hydrogen using the combined effect of light and heat. Photocatalytic production of hydrogen from renewable sources such as alcohols is important to sustainably provide a crucial industrial building block and a promising clean fuel 27 . This is attained by reducing protons to hydrogen and oxidizing carbon-containing compounds to CO 2 via photogenerated electrons and holes in a semiconductor catalyst, a process generally called photoreforming. The use of plasmonic materials has been shown to improve the rate of photocatalytic reactions thanks to higher temperatures developed around the plasmonic structures, typically by the use of a laser 28 29 . But there is a lot of scope for improvement, since cavity enhanced plasmonic structures have not been explored for photocatalysis till now. To show
The search for soft modes in TiPd:Cr revealed some sur- prising features. The 关110兴-TA 2 phonon branch exhibits
anomalous momentum and temperature dependence in that the modes are very broad over nearly the entire Brillouin zone at room temperature. The linewidths of the phonons increase with decreasing temperature at the same time that the energies decrease. Anharmonicity would result in the op- posite behavior, so another type of coupling has to give this result. A clue to this comes from first principles studies of the electronic and phonon structures of TiPd. 8 This type of cal- culation has proven to be very successful in explaining the anomalous phonon behavior in a number of other systems exhibiting martensitic transformations and shape-memory behavior such as NiAl, 16 NiTi, 24 and Ni 2 MnGa. 25 They ac- curately calculate the wave vector of the instability as due to nesting Fermi wave vectors and strong electron-phonon cou- pling, the precise ingredients of a charge density wave. The recent calculations on TiPd 共Ref. 8 兲 reveal an interesting be- havior of the phonon dispersion curves of the cubic B2 phase. These calculations for T = 0 show that many of the acoustic branches have a negative frequency, which implies that the B2 phase is unstable at T = 0 and a phase transfor- mation occurs at finite temperatures. It also implies that the B2 phase is dynamically stabilized by anharmonic phonons and that large fluctuations and local distortions are present in the B2 cubic phase. Of particular interest is the behavior of the 关110兴-TA 2 phonon branch, where the calculations show negative frequencies throughout the Brillouin zone. In con- trast to other systems such as NiAl, NiTi, or Ni 2 MnGa for which there is a well-defined wave vector where the phonon dispersion curve becomes negative, there is no special wave vector for TiPd. The negative frequency for the entire branch is indicative that the branch is anomalous and consistent with the observation of broadening over the entire branch.
Another and quite likely possibility to introduce a temperature-dependent error as observed would be an overestimation of the phonon softening due to the anharmonic ion-ion interactions. While it was demonstrated in case of copper that these effects may be adequately modeled by imposing thermal expansion on the system, this needs not necessarily be true for aluminum, the more so as the upper bound of the employed temperature regime is comparatively close to the melting point. Although we witness in subsection 3.2.1 that the Debye-Grüneisen model is suited to accurately describe the thermal expansion of the solid, the phonon densities of states calculated and measured in reference  may serve as allowedly weak evidence that, by using these lattice constants in both our LDA and GGA calculations, we do not only underestimate the phonon eigenfrequencies, but simultaneously overestimate the attenuation thereof. A continuing analysis of this conjecture is definitely in order, but collapses as we lack detailed, publicly available data on the temperature dependence of the phonon modes in aluminum.
In summary, we combined infrared and optical spectroscopy with high-ﬁeld magnetization and ﬁrst-principles calculations to explore coupling processes involving the fundamental excitations of the lattice in Sr 3 NiIrO 6 — a material with signi ﬁ cant spin – orbit interactions. These include both spin – lattice and electron – phonon processes. Magneto-infrared spectroscopy reveals that three phonons — all of which modulate the magnetic pathways around and the symmetry of the Ir centers — display strong spin – lattice interactions, demonstrating that the approach to the coercive ﬁ eld takes place with very speci ﬁ c local lattice distortions — different from expectations for simple domain reorientation in a ferro- magnet. Examination of the mode displacement patterns also provides a speciﬁc mechanism for inter-chain interactions, a ﬁnding that is crucial to the development of the working magnetic model in Sr 3 NiIrO 6 and related materials. At the same time, analysis of the on-site Ir 4 + excitations unveils vibronic coupling and extremely large crystal ﬁ eld parameters. For instance, 10Dq is a factor of two larger than that in traditional transition metal oxides, and the Racah parameter B is a factor of 10 higher.
In summary, we combined infrared and optical spectroscopy with high-ﬁeld magnetization and ﬁrst-principles calculations to explore coupling processes involving the fundamental excitations of the lattice in Sr 3 NiIrO 6 —a material with signiﬁcant spin–orbit interactions. These include both spin –lattice and electron–phonon processes. Magneto-infrared spectroscopy reveals that three phonons —all of which modulate the magnetic pathways around and the symmetry of the Ir centers —display strong spin–lattice interactions, demonstrating that the approach to the coercive ﬁeld takes place with very speci ﬁc local lattice distortions—different from expectations for simple domain reorientation in a ferro- magnet. Examination of the mode displacement patterns also provides a speciﬁc mechanism for inter-chain interactions, a ﬁnding that is crucial to the development of the working magnetic model in Sr 3 NiIrO 6 and related materials. At the same time, analysis of the on-site Ir 4 + excitations unveils vibronic coupling and extremely large crystal ﬁeld parameters. For instance, 10Dq is a factor of two larger than that in traditional transition metal oxides, and the Racah parameter B is a factor of 10 higher.
superconductor. Thus, knowledge and understanding concerning phonons in these materials are essential. To investigate phonon spectra, Raman and infrared spectra of these systems have been studied; however, there are a few reports available in the literature with complete Raman and infrared absorption spectra. Due to the nature of these superconductive materials, it is not possible to experimentally obtain all of the phonon frequencies through Raman and infrared spectra. Therefore, a theoretical evaluation of the phonon frequencies of hightemperature superconductors becomes important. Due to strong, covalent nature of the bonding in hightemperature superconductors, a normal coordinate analysis using Wilson’s FG matrix was applied herein to evaluate the phonon frequencies of Tl-Ba-Ca-Cu-O. Calculations of lattice dynamics were also performed using the modified three-body-force shell model. The various interactions between ions were treated in a general way without making them numerically equal. These calculations yielded the zone centre phonon modes and potential energy distributions that helped to identify the pure and mixed frequencies.
It is important to note that none of direct interband transitions overlap with the phonon energy. ARPES re- sults in Figure 2 show that the splitting of bands in gra- phene bilayers, close to 0.4 eV, is twice as big as the phonon energy. Therefore, the electronic continuum re- sponsible for Fano interactions has to be connected with non direct transitions. Most likely, a high concentration of hydrogen atoms within graphene buffer layer and probably also between graphene layers allows non-direct optical transitions. It seems that the presence of hydrogen is essential for conservation of momentum in interband electronic transitions and observation of a strong Fano
It is shown that the linear resistivity dependence on temperature for metals above the Debye’s temperature mainly is caused by electron-electron scatter- ing of randomly moving electrons. The electron mean free path in metals at this temperature range is in inverse proportion to the effective density of randomly moving electrons, i.e. it is in inverse proportion both to the tem- perature, and to the density-of-states at the Fermi surface. The general rela- tionships for estimation of the average diffusion coefficient, the average ve- locity, mean free length and average relaxation time of randomly moving electrons at the Fermi surface at temperatures above the Debye’s temperature are presented. The effective electron scattering cross-sections for different metals also are estimated. The calculation results of resistivity dependence on temperature in the range of temperature from 1 K to 900 K for Au, Cu, Mo, and Al also are presented and compared with the experimental data. Addi- tionally in temperature range from 1 K to 900 K for copper, the temperature dependences of the mean free path, average diffusion coefficient, average drift mobility, average Hall mobility, average relaxation time of randomly moving electrons, and their resultant phonon mediated scattering cross-section are presented.
Phonon Precursors to the HighTemperature Martensitic Transformation in Ti50Pd42Cr8
Inelastic neutron scattering measurements were carried out on the Ti50Pd50-xCrx alloy, which has the potential for being a hightemperature shape memory material. For x=0, the transformation temperature is