Charge transport in disordered solids with applications in by Sergei Baranovski

By Sergei Baranovski

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3 3 2π 2 , [8]) and the constants F a0 are the Fermi-liquid interaction parameters (in the triplet channel) that depend on the screening radius. Thus the interaction term has a T 1/2 dependence, but its sign depends on the relative size of the exchange and Hartree terms, which is a function of the screening length. In doped multi-valley semiconductors, such effects as the presence of several conduction band minima, scattering, and mass anisotropy must be considered if a detailed quantitative comparison is desired.

Thus, the fixed point gc separates the regions of the initial conditions corresponding to localized and extended states. The quantity (g0 − gc) / gc may be considered as a parameter that determines the energy separation from the mobility edge. 11) where the parameter v determines the slope of the function b (g) at the point g = gc. 11) is valid. 12) which gives the correct slope of b (g) at g = gc and the correct asymptotic behavior at large L (if vgc = A). Using this expression, we can explicitly perform the integration and find the macroscopic conductivity corresponding to a given initial value g0.

From this, we easily obtain that at large g β (g) ≃ 1 − A g . 19) to the transport equation, related to the backscattering, whose sum logarithmically diverges at small wave vectors k. 9) at large g. 10) where d is the system dimensionality and A is, generally, different for d = 2 and d = 3. 10) and assuming that the function b (g) is continuous and monotonic, we can qualitatively represent its shape in the entire range of variation of g. 4. 4, we see that, for d = 3 (curve a), there is at least one zero of the function b (g), which we denote by gc.

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