The Diagram Technique for Calculation of Transport Constants of Random Inhomogeneous Materials. II. Low‐Field Hall Effect

Diagram methods are applied for evaluating the off‐diagonal (Hall) components of the ac effective magnetoconductivity tensor σ yx*(ω) in an inhomogeneous material for the case of low magnetic field. Closed expressions for σ ik*(ω) are obtained in two approximations, namely in the self‐consistent cumulant approximation and in the effective‐medium approximation (EMA). Our expression for σ ik*(ω) in the EMA coincides with the one obtained earlier by Fishchuk. The obtained results are applied to the model of a random binary mixture consisting of two conducting materials 1 and 2 with conductivity tensors σ ik(1) and σ ik(2) and volume fractions x and 1 − x, respectively. In the special case of σ ik(2) = 0 and ω = 0 the (dc) Hall conductivity σ yx* in both above‐mentioned approximations has a percolation threshold at some critical value X_c. In each approximation the value of x_c coincides with the one for the dc diagonal (ohmic) conductivity σ* taken in the same approximation: the self‐consistent cumulant approximation gives x_c = 1 – exp (−1/3), while in the EMA x_c is equal to 1/3.