Spin splitting and anomalous Hall resistivity in three-dimensional disordered systems

Abstract

We comment on recently observed oscillations of the Hall resistivity around the classical value with particular emphasis on the coexistence of localized and extended states in the case of a spinsplit lowest Landau level. We prove the existence of localization at the bottom of the 0t level, thus explaining the observed plateaulike feature of the Hall resistivity.Although the Shubnikov-de Haas (SdH) oscillations of the magnetoresistance are by now well understood, no convincing theoretical explanation for the oscillatory deviations of the Hall resistivity from the classical behavior has been presented so far. In recent experiments' the Hall resistivity p"~w as investigated in narrow-gap, bulk semiconductors such as InAs, InSb, and Hg~-"Cd,Te with particular emphasis on the magnetic-field region where the last SdH minimum of the longitudinal resistivity p" is observed. The interesting feature was a distinct decrease of the slope of the p"~v ersus 8 graph in the same region. Murzin' was the first to suggest a relation to the quantum Hall eA'ect (QHE) in two-dimensional (2D) systems and conjectured that electron-electron interaction might account for an additional phasea Hao insulatorin three dimensions. Mani tried to reproduce the essential experimental features in a simple model by assuming the existence of localized states at the bottom of each 3D Landau level (LL). His model suggested real plateaus at T=O coinciding with the SdH minima. In Refs. 1 and 2, however, only one plateaulike structure was observed together with the last SdH minimum. From the theoretical point of view three questions arise. (i) Does p, , exhibit plateaus at T=O or is only the slope decreasing? (ii) Can the existence of localized states be proven? How can the problem of coexistence of localized and extended stateswhich was put forward in Ref. 3be solved in the presence of disorder?(iii) Does the magnetic-field range in which the last SdH minimum occurs play a distinguished role concerning the plateaulike feature of p", , ? Finally, we have also to comment on the observation of a Hall resistivity being smaller than the classical value for magnetic fields below the last SdH oscillation as well as before approaching the freezing-out Mott-insulator (MI) transition at high fields.In the following we want to illustrate that the decreasing slope of p, -,, can be understood within a model of 3D disordered systems studied previously, provided spinsplitting is taken into account. Let us first recall that the g factor of InSb decreases from about 50 to 35 for a doping concentration varying from n =10' to 10' cm (cf. , e.g. , Ref. 5). With the eA'ective mass m=0. 014m, this yields a spin splitting of one third of the LL separation so that at least for the lowest Landau level (LLL) the spin splitting is well resolved. Consequently, in the vicinity of the last observed SdH minimum the Fermi energy crosses the bottom of' the 0) level. Since in the absence of magnetic impurities the one-particle states of the lowest spin-up and spin-down LL cannot mix, all...

Vanishing Hall Coefficient in the Extreme Quantum Limit in Photocarrier-DopedSrTiO3

“…Scenarios proposed to explain this feature include inhomogeneous metallic clusters [21], the three-dimensional quantum Hall effect [22], and Zeeman splitting of the lowest Landau level [23]. Although these theories predict a reduction of R H around the critical field for magnetic freeze-out, strong divergence of xx and xy has been experimentally observed, which is absent in our measurements.…”

“…The large m à dictates that the regime of magnetic freeze-out occurs at extremely low temperature and high magnetic field and thus would appear unrelated to the saturation in xy observed here. We also note that the scenarios suggested above are based on magnetic freeze-out starting from a degenerate state [21][22][23], quite unlike our nondegenerate starting point, leading to conceptual and quantitative discrepancies [19]. However, we cannot rule out a similar mechanism driving inhomogeneities for a nondegenerate gas.…”

Magneto-oscillations of the Hall coefficient in n-type GaSb at the extreme quantum limit

“…(ii) The r xy ðBÞ Hall resistivity exhibits small deviations from linearity, with a knee-like structure more pronounced at the lowest temperatures and practically absent at T , 15 K. This behavior results in oscillations of the Hall coefficient R H around the R cl classical value obtained from the low fields slope of the linear r xy ðBÞ dependence. (iii) The amplitude of the R H oscillation is anomalously large near the EQL with the maximum at a field B M which is slightly larger than B EQL : The above results are qualitatively similar to those found in narrow gap semiconductors such as InSb, InAs and HgCdTe [15,18,19,[22][23][24] although in the most of the latter cases the condition r xy . r xx is generally satisfied at high magnetic fields and only in a few cases r xy just approaches r xx ; as in the present one.…”

“…It is known that the oscillating behavior of R H may have different origins and the most natural explanation, based on the oscillatory behavior of the scattering time [16,17], failed to explain the unexpectedly high magnitude of the last maximum in R H : According to Viehwegen et al [23] and Zeitler et al [19] this last feature can be justified by invoking low energy tails where the electrons are localized in the density of states (DOS) of the two lowest spin-split 0 (2 ) and 0 (þ ) LLs. In the absence of spin-flip scattering the two spin-up and spin-down electron systems cannot mix and have to be considered separately; moreover, localized states cannot exist at higher LLs ðn $ 1Þ; since they should coexist with extended states having the same energy and spin.…”

“…[5] and references therein ), n-type doping of bulk crystals grown from the melt is normally limited to the high density range (n $ 10 17 cm 23 ). Differently, GaSb samples with free electron densities as low as a few 10 16 cm 23 have been obtained by molecular beam epitaxy (MBE) [6,7]; however, the minimum donor concentration to obtain n-type conductivity always overcomes the critical density n c for the Mott transition in the G valley (n c , 10 15 cm 23 ). Therefore, at low temperature the electron gas in the G valley is always degenerate.…”