The scattering measurements and first- principles calculations showed that the iron partial vibrational entropy is close to what is predicted by the quasiharmonic approximation owing to [r]

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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.

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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**-**phonon** **interactions** 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.

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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 [14]. 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.

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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.

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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**-**phonon** **interactions**, 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].

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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 [38], the Kohn effect [39], **temperature**-dependent electrical resistivity as well as traditional superconductivity [40] are caused by the **electron**-**phonon** interaction. The role of **electron**-**phonon** **interactions** in the transport properties of systems with strong **electron**-**phonon** correlations is one of the central issues in the theory of strongly correlated systems.

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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 **high** **electron** 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**.

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ABSTRACT
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 **electron** **phonon** linewidth and **electron** **phonon** shift has been obtained. It is established fact that at **high** **temperature** limit when anharmonic effects are dominant, the contributions of harmonic field, localized field, **electron** **electron** interaction field are feeble. It has been found that at **high** **temperature** limit, cubic and quartic parts of **electron** **phonon** linewidth and **electron** **phonon** shift have been matched with the Balkanski et al. model for linewidh and shift at **high** **temperature**. An analysis of first order Raman spectra of germanium has been carried out on taking anharmonicity upto quartic terms.

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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 , **electron** **phonon** interaction part , anharmonic part .The anharmonicity has been taken upto quartic terms . The response function has been obtained responsible for **electron** **phonon** linewidth . At **high** **temperature**, 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.

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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**-**electron** **interactions**, 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. [1] and [64] 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**-**phonon** **interactions**. One also discovers an intrinsic instability of a system at **high** values of **electron**-**phonon** coupling, called Wentzel-Bardeen instability.

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130
a) b)
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

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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.

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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 [108] 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.

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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.

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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.

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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 **high** **temperature** superconductors becomes important. Due to strong, covalent nature of the bonding in **high** **temperature** 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.

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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

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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.

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