Condensed Matter Physics / Materials

The condensed phases of helium three provide an exciting laboratory for many fundamental questions in condensed matter physics. Due to its light mass and weak interatomic potential, the condensed phases of helium display quantum effects more dramatically than any other atomic system. Intuition based on classical experience is often misleading in these phases: the solid phase for instance is less ordered at low temperature than the liquid phase. The book covers all the low temperature properties of helium three as liquid, superfluid, and solid. It provides an introduction to the extensive literature on helium three from the point of view of an experimentalist, and includes the analogy of its properties with the cosmological ‘big bang’.

In materials, critical phenomena such as phase transitions, plastic deformation and fracture are intimately related to self-organization. Understanding the origin of spatio-temporal order in systems far from thermal equilibrium and the selection mechanisms of spatial structures and their symmetries is a major theme of present day research on the structure of continuous matter. Furthermore, the development of methods for producing spatially-ordered and self-assembled microstructure in solids by non-equilibrium methods opens the door to many technological applications. In order to describe and understand the behaviour of such materials, dynamical concepts related to non-equilibrium phenomena, irreversible thermodynamics, nonlinear dynamics, and bifurcation theory, are required. The generic presence of defects and their crucial influence on pattern formation and critical phenomena in extended systems is now well-established. Similar to observations in hydrodynamical, liquid crystal, and laser systems, defects in materials have a profound effect. This book is divided into two volumes. The first volume is devoted to the most basic concepts of the physics, mechanics, and mathematical theory utilized in the analysis of non-equilibrium materials. The book presents a background on material deformation, defect theory, transport processes, and the statistical mechanics and thermodynamics of phase transitions. Mathematical concepts of non-linear dynamics, such as bifurcation and instability theory, the dynamics of complex systems near pattern forming instabilities, the generic aspects of pattern formation, selection and stability are presented. Stochastic and numerical methods used in this field are also introduced. The methods and techniques developed in the first volume are applied in the second volume to specific problems in various advanced technologies.

This book presents high-power terahertz applications to semiconductors and semiconductor structures. It aims to bridge the gap between optics and microwave physics. It focuses on a core topic of semiconductor physics, providing a full description of the state of art of the field. The book introduces new physical phenomena which occur in the terahertz frequency range at the transition from semi-classical physics with a classical field amplitude to the fully quantized limit with photons. It covers tunneling in high-frequency fields, nonlinear absorption of radiation and radiation heating, nonlinear optics in the classical sense, Bloch-oscillations and ponderomotive forces of the terahertz radiation on free carriers, photon drag and photogalvanic effects, and terahertz spin dependent phenomena being of importance in the field of spintronics. Background information for future work and references of current literature are given. The book also discusses various experimental aspects like the generation of high-power coherent terahertz radiation, properties of materials with respect to their application in optical components, and detection schemes of short intense terahertz pulses.

The scanning tunneling microscope (STM) and the atomic force microscope (AFM), both capable of visualizing and manipulating individual atoms, are the cornerstones of nanoscience and nanotechnology today. The inventors of STM, Gerd Binnig and Heinrich Rohrer, were awarded with the Nobel Prize of physics in 1986. Both microscopes are based on mechanically scanning an atomically sharp tip over a sample surface, with quantum-mechanical tunneling or atomic forces between the tip and the atoms on the sample as the measurable quantities. This book presents the principles of STM and AFM, and the experimental details. Part I presents the principles from a unified point of view: the Bardeen theory of tunneling phenomenon, and the Herring-Landau theory of covalent-bond force. The similarity between those two theories, both rooted from the Heisenberg-Pauling concept of quantum-mechanical resonance, points to the equivalence of tunneling and covalent-bond force. The Tersoff-Hamann model of STM is presented, including the original derivation. The mechanisms of atomic-scale imaging of both STM and AFM are discussed. Part II presents the instrumentation and experimental techniques of STM and AFM, including piezoelectric scanners, vibration isolation, electronics and control, mechanical design, tip treatment and characterization, scanning tunneling spectroscopy, and atomic force detection techniques. Part II ends with illustrative applications of STM and AFM in various fields of research and technology.

Modelling of heterogeneous processes, such as electrochemical reactions, extraction, or ion-exchange, usually requires solving the transport problem associated with the process. Since the processes at the phase boundary are described by scalar quantities and transport quantities are vectors or tensors, the coupling of them can take place only via conservation of mass, charge, or momentum. In this book transport of ionic species is addressed in a versatile manner, emphasizing the mutual coupling of fluxes in particular. Treatment is based on the formalism of irreversible thermodynamics, i.e., on linear (ionic) phenomenological equations, from which the most frequently used Nernst-Planck equation is derived. Limitations and assumptions made are discussed in detail. The Nernst-Planck equation is applied to selected problems at the electrodes and in membranes. Mathematical derivations are presented so that the reader can learn the methodology of solving transport problems. Each chapter contains a large number of exercises.

In liquid helium, an electron is surrounded by a cavity called an electron bubble of 20 Ångstroms in diameter. A positive helium ion is solvated by an electrostriction induced solid helium-ice shell called a snowball of 7 Ångstroms in diameter. By studying their transport properties, these objects are well suited for the testing of the microscopic properties of superfluidity. At low temperatures and with small electric fields, the drift velocity of the charges depends on their interaction with the elementary excitations of the superfluid: phonons, rotons, and ³He atomic impurities. At higher fields, ions produce quantized vortex rings and vortex lines and studying these sheds light on quantum hydrodynamics. In the fermionic liquid, the ³He isotope ion transport properties display important pieces of information on the coupling of a charge to a Fermi liquid and on the richer topological structure of the superfluid phases appearing at ultralow temperatures. In the normal liquid phases of both isotopes, ions and electrons are used to probe classical hydrodynamics at the λ-transition and at the liquid-vapor transition at which long-range critical fluctuations of the appropriate order parameter occur. Several experiments have investigated the structure of electron bubbles. Electron drift velocity measurements in dense helium gas have elucidated the dynamics of electron bubble formation. This book provides a review of the more than forty-year-long experimental and theoretical research on the transport properties of electrons and ions in liquid and gaseous helium.

Kinetic Theory of Granular Gases provides an introduction to the rapidly developing theory of dissipative gas dynamics — a theory which has mainly evolved over the last decade. The book is aimed at readers from the advanced undergraduate level upwards and leads on to the present state of research. Throughout, special emphasis is put on a microscopically consistent description of pairwise particle collisions which leads to an impact-velocity-dependent coefficient of restitution. The description of the many-particle system, based on the Boltzmann equation, starts with the derivation of the velocity distribution function, followed by the investigation of self-diffusion and Brownian motion. Using hydrodynamical methods, transport processes and self-organized structure formation are studied. An appendix gives a brief introduction to event-driven molecular dynamics. A second appendix describes a novel mathematical technique for derivation of kinetic properties, which allows for the application of computer algebra. The text is self-contained, requiring no mathematical or physical knowledge beyond that of standard physics undergraduate level. The material is adequate for a one-semester course and contains chapter summaries as well as exercises with detailed solutions. The molecular dynamics and computer-algebra programs can be downloaded from a companion web page.

Layered Superconductors, Volume I, describes the chemistry and physics of all layered superconductors. Although widespread interest in the subject did not really arise until the discovery of high-temperature superconductivity in the cuprates, it has a much longer history, and is still evolving rapidly. This book describes the chemical syntheses, crystal structures, calculations and measurements of the Fermi surfaces, and measurements of the normal state physical properties and of the upper and lower critical fields of all classes of layered superconductors. At present, the large classes of layered superconductors are the graphite intercalation compounds, the transition metal dichalcogenides, the intercalated transition metal dichalcogenides, the organic layered superconductors,various artificial superconducting superlattices, the cuprates, binary and ternary intermetallics with the AlB₂ structure, ternary and quaternary intermetallics of the ThCr₂Si₂ structure, the borocarbides, the iron pnictides, the iron oxypnictides, and the iron chalcogenides. Each of the stoichiometric compounds Sr₂RuO₄, MgB₂, La₃Ni₂B₂N₃, and Ag₅Pb₂O₆ are layered superconductors, as are intercalated β-ZrNCl and β-HfNCl. Many of these materials exhibit electronic instabilities such as charge-density waves, spin-density waves, magnetism, and “pseudogaps”, which may have closely related origins, and which compete with the superconductivity. Some of these materials are extremely anisotropic, while others are nearly isotropic in their normal and superconducting behaviours. To characterize the superconductivity, three phenomenological models are presented: the anisotropic London model, the anisotropic Ginzburg-Landau model, and the Lawrence-Doniach model. These models are used to calculate the upper and lower critical fields of layered superconductors. Experimental verification of these and selected microscopic models is provided.

Nanomagnetism is a rapidly expanding area of research in nanoscience, opening perspectives of novel applications. Magnetic molecules are at the very bottom of the possible size of nanomagnets, and they provide a unique opportunity to observe the coexistence of quantum and classical properties. The discovery in the early 1990s that a cluster comprising twelve manganese ions shows magnetic hysteresis of molecular origin accompanied by quantum tunnelling of the magnetization opened a new research, which is flourishing through the collaboration of chemists and physicists. The field is often indicated as single molecule magnets (SMM). This book attempts to cover in detail the area of molecular nanomagnetism — a branch of molecular magnetism — using a language which should be understood by both the physical and chemical communities. The book starts from the development of theory needed to understand the nature of the properties of molecular nanomagnets, including magnetic coupling and magnetic anisotropy. The most common experimental techniques needed to investigate the properties of molecular nanomagnets are covered to allow the reader to understand how sophisticated instrumentation can provide unique information on SMM. Particular attention is devoted to magnetic relaxation, highlighting the interplay of classical and quantum behaviours. Appendices cover topics which would require too many digressions in the main text, ranging from systems of units to master equations for the density matrix.

The book opens with three chapters describing the properties of atoms. The first chapter deals with the application of quantum mechanics to hydrogen and other one-electron atoms; the second with the use of the atomic orbital model to describe He and other two-electron atoms; the third gives an overview of the electron configurations, ground state energies, ionization energies, electronegativity coefficients, and atomic sizes of poly-electron atoms. The following six chapters deal with the properties of diatomic molecules, in particular their bond distances, dissociation energies, electric dipole moments, and estimated net atomic charges. The molecular structures of compounds of the elements in Groups 2 and 12, and in Groups 13 through 18 are described in separate chapters, with particular emphasis on hydrogen, methyl, and halogen derivatives. The main emphasis is on equilibrium structures, but bond energies are included in the discussion whenever available, and large amplitude motion like the inversion of amines, pseudorotation in five-coordinate species, or intermolecular rearrangements through rapid dissociation and recombination are discussed. The structures of electron deficient molecules and of electron donor-acceptor complexes are described in separate chapters. The final chapter discusses the structures and bonding in oxides and oxoacids of carbon, sulfur, nitrogen phosphorus, and chlorine. Throughout the book, models concepts like the spherical ion model, the electron pair bond, Lewis structures, atomic bonding radii, the valence shell electron pair repulsion (VSEPR) model, or the molecular orbital model are introduced as the need arises. Attention is paid to both the successes and failures of each model.