Non-Linear and Non-Equilibrium Properties of Two-Dimensional Disordered Systems. I : Conductivity

概要

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The non-linear dependences of the non-metallic part of conductivity σ' on uniform electric and magnetic fields, E and H, are investigated in two-dimensional disordered systems. We calculate (i) σ' (T,E), (ii) σ' (T,H) and (iii) σ' (T,E,H) in the crossing fields E⊥H. There exist two kinds of the characteristic fields of non-linearity : E_0 = √<6>h/eτl and H_0 = ch/el^2, which are independent of temperature T, and E_0 (T) 0 E_0η^<3/2> and H_0 (T) = H_0η, which depend on T. Here η = τ/<τ_ε> (T), τ and l are the relaxation time and mean free path due to the elastic impurity scattering, and τ_ε is the energy relaxation time. We show that (1) σ'(T, E) behaves like ln (E/E_0) in E_c(T) ≪E≪E_0, (2) σ'(T, H) behaves like ln (H/H_0) in H_c(T) ≪H≪H_0, (3) both approach ln η in E≪E_c(T) and H≪H_c(T) respectively, (4) σ' (T, E, H) depends still logarithmically, though a little weakened, on the respective fields in their ranges of intermediate strengths, and (5) σ' (T,E,H) crosses over to σ' (T, H) or σ' (T, E) as E or H is weakened. Recent experiments on σ' (T, E) are explained by our theory qualitatively. The possible log E dependence of the excess conductivity of a superconducting film is studied in the Appendix.
理論物理学刊行会の論文
1982-01-25