Hall effect theoretical predictions

The work of Halls and Schlegel illustrates particularly effectively how different levels of theory may be used for studying different aspects of a complex chemical problem. Furthermore, repeated comparisons of theoretical predictions to experimental measurements in order to validate tire chosen levels of theory provides solid support for the quality of further predictions using those levels. 

Quantum-electrodynamics (QED) as the fundamental theory for electromagnetic interaction seems to be well understood. Numerous experiments in atomic physics as well as in high energy physics do not show any significant discrepancy between theoretical predictions and experimental results. The most striking example of agreement between theory and experiment represents the g factor of the free electron. The experimental value of g = 2.002 319 304 376 6 (87) [1] is confirmed by the calculated value of g = 2.002 319 304 307 0 (280) on the 10 11-level, where the fine structure constant as an input in the theoretical calculation was taken from the quantum Hall effect [2], Up to now uncalculated non-QED contributions play no important role. Indeed today experiment and theory of the free electron yield the most precise fine structure constant. 

Fig. 4. The Mott-Schottky plot for the a = 0.025 crystal of Fig. 1. The dotted line shows the theoretical slope predicted from the room temperature Hall effect and conductivity measurements. The slope at strongly anodic bias (V positive) is a measure of the total donor density in this crystal.

Theoretical calculations predict significant anisotropy in effective hole masses for the different valence bands of GaN, though the various calculations differ in the predicted magnitude of the anisotropy in each band [113-115]. Direct measurements of hole masses are, however, very difficult and most reported experimental values are indeed inferred from luminescence, magneto-optical studies of exciton luminescence, infrared reflectance and transmittance studies of polar materials, which are often isotropically averaged and thus not informative about the anisotropy. Directionally dependent Hall-effect measurements in m-plane GaN films grown on m-plane SiC substrates... 

---