Phonons and electrons are two types of excitations which are responsible for many properties of condensed matter materials. The interaction between them plays an important role in condensed matter physics. In this thesis we present some theoretical investigations of the effects due to the interactions between phonons and electrons interactions. We show evidence that a structural martensitic transition is related to significant changes in the electronic structure, as revealed in thermodynamic measurements made in high magnetic fields. The effect of the magnetic field is considered unusual, as many influential investigations of martensitic transitions have emphasized that the structural transitions are primarily lattice dynamical and are driven by the entropy due to the phonons. We provide a theoretical frame-work which can be used to describe the effect of a magnetic field on the lattice dynamics in which the field dependence originates from the dielectric constant. The temperature-dependence of the phonon spectrum of alpha-uranium has recently been measured by Manley et al. using inelastic neutron scattering and x-ray scattering techniques. Although there is scant evidence of anharmonic interactions, the phonons were reported to show some softening of the optic modes at the zone boundary. The same group of authors later reported that an extra vibrational mode was observed to form at a temperature above 450 K. The existence of the proposed new mode is inconsistent with the usual theory of harmonic phonons, as applied to a structure composed of a monoclinic Bravais lattice with a two-atom basis. We investigate the effect that the f electron-phonon interaction has on the phonon spectrum and its role on the possible formation of a breathing mode of mixed electronic and phonon character. We examine the model by using Green's function techniques to obtain the phonon spectral density. Some materials undergo phase transitions from a high temperature state with periodic translational invariance to a state in which the electronic charge density is modulated periodically. The wave vector of the modulation may be either commensurate or incommensurate with the reciprocal lattice vectors of the high temperature structure. In the case of an incommensurate charge density wave, the system supports phason excitation. For an incommensurate state, the new ground state has a lower symmetry than the high temperature state since the charge density does not have long-ranged periodic translational order. If the metal is ideal (with no impurities), a charge density wave should be able to slide throughout the crystal without resistance, resulting in current flow similar to that of a superconductor. The phason is an excitation of the charge density wave which is related to the collective motion of electrons. We estimate the phason density of states, and the phason contribution to the specific heat. Angle-resolved photoemission experiments have been performed on USb2, and very narrow quasiparticle peaks have been observed in a band which local spin-density approximation (LSDA) predicts to osculate the Fermi energy. The observed band is found to be depressed by 17 meV below the Fermi energy. The experimentally observed quasiparticle dispersion relation for this band exhibits a kink at an energy of about 23 meV below the Fermi energy. The kink is not found in LSDA calculations and, therefore, is attributable to a change in the quasiparticle mass renormalization by a factor of approximately 2. The existence of a kink in the quasiparticle dispersion relation of a band which does not cross the Fermi energy is unprecedented. The kink in the quasiparticle dispersion relation is attributed to the effect of the interband self-energy involving transitions from the osculating band into a band that does cross the Fermi energy.

The characteristics of electrical contacts have long attracted the attention of researchers since these contacts are used in every electrical and electronic device. Earlier studies generally considered electrical contacts of large dimensions, having regions of current concentration with diameters substantially larger than the characteristic dimensions of the material: the interatomic distance, the mean free path for electrons, the coherence length in the superconducting state, etc. [110]. The development of microelectronics presented to scientists and engineers the task of studying the characteristics of electrical contacts with ultra-small dimensions. Characteristics of point contacts such as mechanical stability under continuous current loads, the magnitudes of electrical fluctuations, inherent sensitivity in radio devices and nonlinear characteristics in connection with electromagnetic radiation can not be understood and altered in the required way without knowledge of the physical processes occurring in contacts. Until recently it was thought that the electrical conductivity of contacts with direct conductance (without tunneling or semiconducting barriers) obeyed Ohm's law. Nonlinearities of the current-voltage characteristics were explained by joule heating of the metal in the region of the contact. However, studies of the current-voltage characteristics of metallic point contacts at low (liquid helium) temperatures [142] showed that heating effects were negligible in many cases and the nonlinear characteristics under these conditions were observed to take the form of the energy dependent probability of inelastic electron scattering, induced by various mechanisms.

This NATO Advanced Study Institute was the fourth in a series devoted to the subject of phase transitions and instabilities with particular attention to structural phase transforma~ions. Beginning wi th the first Geilo institute in 19'(1 we have seen the emphasis evolve from the simple quasiharmonic soft mode description within the Landau theory, through the unexpected spectral structure re presented by the "central peak" (1973), to such subjects as melting, turbulence and hydrodynamic instabilities (1975). Sophisticated theoretical techniques such as scaling laws and renormalization group theory developed over the same period have brought to this wide range of subjects a pleasing unity. These institutes have been instrumental in placing structural transformations clearly in the mainstream of statistical physics and critical phenomena. The present Geilo institute retains some of the counter cul tural flavour of the first one by insisting whenever possible upon peeking under the skirts of even the most successful phenomenology to catch a glimpse of the underlying microscopic processes. Of course the soft mode remains a useful concept, but the major em phasis of this institute is the microscopic cause of the mode softening. The discussions given here illustrate that for certain important classes of solids the cause lies in the electron phonon interaction. Three major types of structural transitions are considered. In the case of metals and semimetals, the electron phonon interaction relie6 heavily on the topology of the Fermi surface.

This monograph is a radical departure from the conventional quantum mechanical approach to electron-phonon interactions. It translates the customary quantum mechanical analysis of the electron-phonon interactions carried out in Fourier space into a predominantly classical analysis carried out in real space. Various electron-phonon interactions such as the polar and nonpolar optical phonons, acoustic phonons that interact via deformation potential and via the piezoelectric effect and phonons in metals, are treated in this monograph by a single, relatively simple “classical” model. This model is shown to apply to electron interactions with the deep lying X-ray levels of atoms, with plasmons and with Cerenkov radiation. The unifying concept that applies to all of these phenomena is a new definition of a coupling constant. The essentially classical interaction of an electron with its surrounding is clearly brought out to be the cause of spontaneous emission of phonons. The same concept also applies to the case of spontaneous emission of photons. While the bulk of this monograph deals with quanta of phonons and quanta of photons, a discussion of the acousto electric effect which is a purely classical phenomenon is presented. The newly defined coupling constant turns out to be valid too for this discussion. This universality of the coupling constant goes far beyond. It is equally applicable to amorphous materials. This significant application gives an analytic formulation of mobility in amorphous materials.

This report presents several contributions to the formulation, calculation and understanding of the effects of electron-phonon interaction in metals with variation in the electronic density of states on the scale of a typical phonon energy. The A15 compound Nb3Sn is studied in detail with this theory. (Author).

The effect of electron phonon interaction on the temperature dependence of paramagnetic susceptibility was examined. This effect should be substantial above the Debye temperature. When taking into consideration the electron phonon interaction, the calculated Fermi energy is a linear function of temperature above the Debye temperature. (Author).

The story of heavy fermions (HF) begun with the discovery of the low temperature behaviour of CeAl3 by Andres et al. in the year 1975 took the momentum after the discovery of superconductivity in CeCu2Si2 by Steglich et al. in the year 1979 . Though HF behaviour is common in the rare-earth elements like Ce, Yb and actinides like U, it is also found to exist in some of the praseodymium (Pr), samarium (Sm) , plutonium (Pu) and more recently in neptunium (Np) systems. These compounds are characterized by the presence of partially filled f-electron bands. At high temperatures, these magnetic moments manifest themselves as a weakly interacting set of local moments of the f electrons with Curie-Weiss susceptibility that coexists with light s or d conduction electrons. But at low temperature, these f-electrons hybridize with conduction electrons near Fermi level via Kondo spin fluctuation which happens through constant exchange spin-flip transition of f-electrons and band electrons in the vicinity of Fermi level. This process leads to a strong mixing of Fermi electrons with the localized f-electrons which is manifested in a renormalization of the Fermi surface and a drastic enhancement of the effective mass of the electrons at Fermi level. Further, in HF systems, electron-phonon interaction (EPI) contributes a lot in manifestation of some of the anomalous behaviour relating to elastic constant, ultrasonic attenuation & sound velocity, anisotropic Fermi surface, Kondo volume collapse etc. In this PhD thesis book in title “Electron phonon interaction and its effect in heavy fermion (HF) systems” the author tries to put some light into the behavoiour of Electron-phonon interaction in describing some of the properties of HF systems at low temperatures. In this 1 st edition, the book has been presented in multicolour edition with profuse colour illustrations so as to increase its clarity, understand ability and legibility, especially of the figures depicted to explain the low temperature behaviour of HF systems. It is hoped that the present book will serve its purpose in attracting young researchers to the field of HF systems. It is my foremost duty to express my deep sense of gratitute to my supervisor Dr. Pratibindhya Nayak , Professor Emeritus, School of Physics, Sambalpur University, Odisha, for his able guidance at every stage of this work.. His innovative methods and inspirational guidance have largely contributed to the conceptualization of the form and content of this book. I am indebted to my family members for their constant support. I am sincerely thankful to the publisher, Newredmars Education to bring my works into light in form of a book Healthy criticism and suggestions for further improvement of the book are solicited.