Quantum Theory of Conducting Matter: Newtonian Equations of Motion for a Bloch Electron

ISBN-13: 9781441925473 / Angielski / Miękka / 2010 / 266 str.

Shigeji Fujita; Kei Ito

Opis

The measurements of the Hall coe?cient R and the Seebeck coe?cient H (thermopower) S are known to give the sign of the carrier charge q. Sodium (Na) forms a body-centered cubic (BCC) lattice, where both R and S are H negative, indicating that the carrier is the electron. Silver (Ag) forms a face-centered cubic (FCC) lattice, where the Hall coe?cient R is negative H but the Seebeck coe?cient S is positive. This complication arises from the Fermi surface of the metal. The electrons and the holes play important roles in conducting matter physics. The electron ( hole ), which by de?- tion circulates counterclockwise (clockwise) around the magnetic ?eld (?ux) vector B cannot be discussed based on the prevailing equation of motion in the electron dynamics: dk/dt = q(E +vxB), where k = k-vector, E = electric ?eld, and v = velocity. The energy-momentum relation is not incorporated in this equation. In this book we shall derive Newtonian equations of motion with a s- metric mass tensor. We diagonalize this tensor by introducing the principal masses and the principal axes of the inverse-mass tensor associated with the Fermi surface. Using these equations, we demonstrate that the electrons ( holes ) are generated, depending on the curvature sign of the Fermi s- face. The complicated Fermi surface of Ag can generate electrons and holes, and it is responsible for the observed negative Hall coe?cient R H and positive Seebeck coe?cient S."

Spis treści

I. Preliminaries Chapter 1 through 5 - Introduction, Theoretical Background; Lattice vibrations, heat capacity; Free electron model, heat capacity; Electrical conduction and the Hall effect; Magnetic susceptibility II. Bloch Electron Dynamics Chapter 6 through 10 - Introduction; The Bloch theorem; The Fermi liquid model; The Fermi surface and de Haas-van Alphen oscillations; Newtonian equations of motion III. Applications Chapter 11 through 18 - Introduction; Cyclotron resonance; Dynamic conductivity, infrared faraday effect; Thermoelectric power; The doping dependence of the susceptibility in cuprates; Electron-phonon interation; Superconductivity; Quantum Hall effect

O autorze

Shigeji Fujita is Professor of Physics at State University of New York at Buffalo and has published 3 books with the Springer family since 1996.  His areas of expertise include statistical physics, solid and liquid state physics, superconductivity and Quantum Hall Effect theory. 

Kei Ito is also a Professor of Physics at the State University of New York at Buffalo, while on leave from the National Center for University Entrance Examinations in Tokyo, Japan.

Blurb

Quantum Theory of Conducting Matter: Newtonian Equations of Motion for a Bloch Electron targets scientists, researchers and graduate-level students focused on experimentation in the fields of physics, chemistry, electrical engineering, and material sciences. It is important that the reader have an understanding of dynamics, quantum mechanics, thermodynamics, statistical mechanics, electromagnetism and solid-state physics. Many worked-out problems are included in the book to aid the reader's comprehension of the subject.

The Bloch electron (wave packet) moves by following the Newtonian equation of motion.  Under an applied magnetic field B the electron circulates around the field B counterclockwise or clockwise depending on the curvature of the Fermi surface. The signs of the Hall coefficient and the Seebeck coefficient are known to give the sign of the major carrier charge.  For alkali metals, both are negative, indicating that the carriers are "electrons."  These features arise from the Fermi surface difference.  The authors show an important connection between the conduction electrons and the Fermi surface in an elementary manner in the text.  No currently available text explains this connection.  The authors do this by deriving Newtonian equations of motion for the Bloch electron and diagonalizing the inverse mass (symmetric) tensor.

The currently active areas of research, high-temperature superconductivity and Quantum Hall Effect, are important subjects in the conducting matter physics, and the authors plan to follow up this book with a second, more advanced book on superconductivity and the Quantum Hall Effect.