The degenerate electron gas in tungsten bronzes and in highly doped silicon

Abstract

New experimental evidence about metallic conduction in tungsten bronzes (Na _x WO₃) is examined, including that due to Lightsey, Lilienfeld and Holcomb (1976) on the Hall coefficient R _H near the lower limit of the metallic cubic phase (x ≃ 0·2). As x approaches this value, 1/R _H drops by about three below the classical value nec, and this is explained as the effect predicted by Friedman (1971) for an electron gas in a strongly non-crystalline field. It is concluded that, both for the cubic bronzes near x = 0·2 and the tetragonal bronzes near x = 0·1, the random field of the charged ions is near the strength needed to produce Anderson localization. Tungsten bronzes thus provide a third example, in addition to expanded fluid mercury and metal-ammonia (cf. Mott 1974), for which the Friedman effect is observed. For tungsten bronzes the evidence suggests that correlation (the Hubbard U) plays little role in producing localization. For doped semiconductors such as Si : P it is usually supposed that the reverse is the case, that is to say that the magnitude of the Hubbard U determines the concentration at which the metal-insulator transition occurs. Certain evidence, particularly the absence of an appreciable Friedman effect in Si : P near the metal-insulator transition, leads us to examine the hypothesis that this may not be so; an Anderson transition due to the random positions of the donors seems equally capable of explaining the data, and in addition may lead to a Friedman effect much smaller than that described above, as is observed. It is suggested that measurements of the thermo-power over a range of compositions which includes that of the metal-insulator transition would give a decisive test.