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Localization phenomena in SnO2 films

The phenomenon of quantum interference in disordered conductors is well known and its effects on the electrical conductance are widely used to determine the inelastic scattering time of charge carriers and, thus, the mechanisms of inelastic scattering. Because of the prominent effects of weak localization in 2D systems, the last became an object of intensive studies. But, the reduced dimensionality and the presence of disorder lead not only to enhancement of interference effects, but also to the necessity to take into account the electron-electron interaction. It appeared that such characteristics as density of states, temperature and magnetic field dependences of electrical conductance could be described only if one takes into account the effects of electron-electron interaction in a disordered low-dimensional system [1]. Moreover, the dephasing mechanisms in weak localization are strongly related to interaction effects: inelastic electron-phonon scattering, quasielastic electron-electron scattering with small energy transfer. The interplay of interference and interaction effects remains a puzzling problem that is still far from being solved [2].

In our SnO2 polycristalline films the low transverse magnetic field dependencies of conductance is positive and can be described in the frame of a 2D weak localization model, the phase breaking mechanism being electron-electron scattering with small energy transfer (not shown here). In Fig.1, the dependencies of magnetoconductance on the normalized magnetic field B/Bφ , measured on the same sample, are presented in the full range of applied magnetic field up to 50 Tesla. Here, Bφ (T) is the value of magnetic field at which the flux of magnetic field through an area enclosed by the electron’s paths becomes equal to the flux quantum h/2e. From both the inset, where the curves are presented in linear coordinates, and from the main part of Fig. 1, one can see that at high fields (starting from 8 Tesla) the curves exhibit different behaviour and do not overlap any more. We thus suggest the necessity to take into account of the anisotropy of scattering potentials in order to describe the observed results. Different particularities of single scattering events may influence (manifest) at different temperatures in this high field region. The experimental curves in Fig. 1 resemble those derived by Zduniak A. et al. [3] and by Germanenko et al. [4] where the weak localization model is extended beyond the diffusion limit. In the frame of this model, only small closed loops are believed to give contribution to the effect of weak localization at such high magnetic fields, the minimum number of collisions in each loop being 3. One can suppose that relative to electron-electron interaction effects, these triangles should be easier to study than any complicated electron’s path with large number of collision. As in many materials the dephasing in the weak localization effet was found to be due to electron-electron interactions, the study of these materials in high magnetic fields should provide important information about these interactions (single electron’s wave function interferece is destroyed, so the interaction effects should give the main contribution to magnetoconductance).

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Fig. 1 The magnetic field dependencies of magnetoconductance as a function of normalized magnetic field. Inset shows field dependencies of magnetoresistance in linear coordinates measured on the same sample.

The problem of electron-electron interaction in disordered systems is still experimentally investigated, but, nevertheless, it persist many unsolved questions. Especially important is the question about equivalence of the so-called Nyquist mechanism of electron-electron interactions involving small energy transfer and the interaction of an electron with the time and space dependent fluctuating electromagnetic fields produced by all the other electrons in the system. The analysis of high-field magnetoresistance data, obtained on our samples of SnO2 polycrystalline thin films, will provide another one possibility to justify the mechanism of electron-electron interaction in disordered systems. The advantage of our samples is in highly controlable degree of disorder, which provides possibility to tune the range of realization of quantum interference under applied magnetic fields. Thus, as we have data obtained in transverse high magnetic fields, we have to carry out the measurements in parallel geometry in order to verify the presence of weak localization effect (in a 2D system it is known to be anisotropic) and extract the partial contributions of the magnetotransport mechanisms. These assertions need to be improved by analysing more samples with different size and distribution of cristallites.

References: [1] Altshuler B.L., Aronov A.G. « Electron-electron interaction in disordered conductors » in Modern problems in condensed matter sciences Vol 10, Efros A.L. & Pollak M. ed., North Holland 1985

[2] Pagnosin I.R., Meikap A.K., Lamas T.E., Gusev G.M., Portal J.C. Phys Rev B 78, 115311 (2008)

[3] Zduniak, A. Dyakonov M.I., Knap W. Phys Rev B 56, 1996 (1997)

[4] Germanenko A.V., Minkov G.M., Sherstobitov A.A., Rut O.E. Phys Rev B 73, 233301 (2006)