The Calculations of Metallic Hall Constants: Topological Aspects and Applications to Copper

When a current-carrying metallic sample is placed in a uniform magnetic field, a change in the resistance is generally observed. This phenomenon, known as magnetoresistance, is the basis for an important experimental technique for studying the band structure of metals. If a simple model is taken to represent a metal (i.e., an effective mass approximation, a constant relaxation time, etc.), then the expected change in resistance can be theoretically predicted. Even with a more realistic model, it is found that one experimentally observable feature can still be predicted, namely, the Hall constant. The analytical expression for the Hall constant [presented in (4)] is an integral over a family of parallel two-dimensional planes. For each plane the integrand is pro1340 13f)0 T H E BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1901 Fig. 1 -- Several F e r m i energy contours, shown in h e a v y lines, g e n e r a t e d by the intersection of the plane Pz = c o n s t a n t with a hypothetical c o n s t a n t e n e r g y surface.