Sign reversal of the effective Hall coefficient in laminates

In the theory of composites, hierarchical laminate microstructures are known to often show optimal behavior. In this paper, their performance in the context of 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---they can mimic the behavior of chain-mail-inspired composites, which exhibit a sign inversion of the effective Hall coefficient. To obtain such a hierarchical laminate, a two-step strategy is used: In the first step, a rank-three laminate with an effective $S$ tensor that has a sign-inverted trace is introduced. In the second step, the final isotropic hierarchical laminate is obtained from the rank-three laminate using an idea of Schulgasser's. As measured by the conductivity contrast required for the inversion as well as by the modulus of the obtained sign-inverted Hall coefficient, the identified hierarchical laminate performs better than the previously studied chain-mail-inspired composites.