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The Diagram Technique for Calculation of Transport Constants of Random Inhomogeneous Materials. II. Low‐Field Hall Effect
Author(s) -
German A. I.,
Chaikovskii I. A.
Publication year - 1993
Publication title -
physica status solidi (b)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.51
H-Index - 109
eISSN - 1521-3951
pISSN - 0370-1972
DOI - 10.1002/pssb.2221800215
Subject(s) - condensed matter physics , conductivity , diagonal , hall effect , percolation (cognitive psychology) , born approximation , physics , diagram , magnetic field , mathematical analysis , mathematics , electron , quantum mechanics , geometry , statistics , neuroscience , biology
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.