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In the theory of composites, hierarchical laminate microstructures are knownto often show optimal behavior. In this paper, their performance in the contextof the Hall effect is evaluated. Using numerical calculations, it is shown that- despite the fact that they are the result of a simple layering process - theycan mimic the behavior of chain-mail-inspired composites, which exhibit asign-inversion of the effective Hall coefficient. To obtain such a hierarchicallaminate, a two-step strategy is used: In the first step, a rank-three laminatewith an effective $S$-tensor that has a sign-inverted trace is introduced. Inthe second step, the final isotropic hierarchical laminate is obtained from therank-three laminate using an idea of Schulgasser's. As measured by theconductivity contrast required for the inversion as well as by the modulus ofthe obtained sign-inverted Hall coefficient, the identified hierarchicallaminate performs better than the previously studied chain-mail-inspiredcomposites.

Sign reversal of the effective Hall coefficient in laminates