Early history

Soon after J. J. Thomson's discovery of the electron in 1897, Drude (1900) showed that most of the characteristic features of a metal could be understood, at least qualitatively, by supposing that some of the electrons were able to move freely through the metal, and a few years later Lorentz worked out the theory more rigorously on the basis of classical statistical mechanics. The outstanding quantitative success of this Drude – Lorentz theory was the explanation it gave of the Wiedemann – Franz law, the proportionality to absolute temperature T, of the ratio of thermal to electrical conductivity. Moreover the predicted constant of proportionality came out close to the experimental value (though less close in Lorentz's more rigorous calculation). However the theory was quite unable to explain why the free electrons did not make a large contribution to the specific heat and later, when electron spin had been discovered, it was not clear why the free electrons did not contribute a large paramagnetic susceptibility varying as 1/T.

It is just over 50 years ago that Pauli (1927) made a major breakthrough by showing that if the recently discovered Fermi–Dirac statistics were used rather than classical statistics in working out the theory, the difficulty about spin susceptibility essentially disappeared. The calculated paramagnetic susceptibility then became independent of temperature and much feebler, roughly comparable to the experimental value.

Introduction

As outlined in the historical introduction (chapter 1), a slight but puzzling discrepancy between the early experimental results on the de Haas–van Alphen oscillations in Bi (Shoenberg 1939) and Landau's theoretical formula was that the observed field and temperature dependences of the amplitude could not be consistently reconciled with the formula. To a fair approximation it was as if the temperature needed to fit the formula was higher than the actual temperature. An explanation of the discrepancy was suggested by Dingle (1952b) who showed (as discussed in §2.3.7.2) that if electron scattering is taken into account, the Landau levels are broadened and this leads to a reduction of amplitude very nearly the same as would be caused by a rise of temperature from the true temperature T to T + x. This extra temperature, x, which is needed to reconcile theory and experiment, has come to be known as the Dingle temperature and we shall refer to the amplitude reduction factor exp(- 2π2kx/βH) as the Dingle factor. Dingle's suggestion also explained an earlier puzzling observation, which was that addition of any impurity to Bi always reduced the oscillation amplitude (Shoenberg and Uddin 1936); this would be expected in view of the increased probability of electron scattering.

For a good many years Dingle temperatures were recorded somewhat casually in studies devoted mainly to FS determinations from frequency measurements, but no systematic studies were attempted and there was little attempt to interpret such results as there were.