Quantum Theory of Conducting Matter
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 +v×B), 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.
Current solid-state physics books say very little about the dynamics of Bloch electrons, and this book will help users to learn and master the issueThe book brings together various modern concepts at the forefront of condensed matter physics including the connection between conduction electrons and the Fermi surfaceThe book will be followed up by a more advanced book on superconductivity and the Quantum Hall Effect