Universal Relations between Conductivity and Dielectric Constant at Anderson Transition

抄録

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−x_c|^s and χ₀|x−x_c|^−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.