Universal Relations between Conductivity and Dielectric Constant at Anderson Transition

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Abstract

Behaviors of conductivity and dielectric constant near Anderson transition are investigated within one-electron theory using renormalization group technique. It is shown that conductivity and dielectric constant depend on a controllable parameter x like σ0|x−xc|s and χ0|x−xc|−2s, respectively, and that the prefactors satisfy the relation σ0\sqrtχ0=C\sqrtν0 where ν0 is the density of state at Fermi level and C is a constant which is independent of the details of the microscopic structure of the system. In the absence of magnetic field and magnetic scattering of electrons, for instance, C is e3(2⁄π3)1⁄2⁄h.

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