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. 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.

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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.