Semiconductors, Metals and Insulators

For problems involving simulations or theory of hyperfine interactions in materials, it would be convenient to work in dimensionless coordinates of reasonable magnitude. The length scale should be approximately a lattice parameter. The time scale should be approximately an inverse hyperfine frequency. The energy scale should be approximately a hyperfine splitting energy. The scale for electric charge should be approximately the elementary electronic charge. The scale for electric field gradients (EFGs) should be approximately as observed in materials (e.g. 1019 to 1021 V/m2). Similarly for magnetic hyperfine fields. There are too many constraints here to allow for an ideal, universal dimensionless unit system. Nevertheless, we can define a useful “natural” dimensionless unit system that simplifies point-charge approximations, scaling between different crystal structures, scaling charges of various defects in materials, and other computations involving hyperfine interactions. We present the proposed system with examples of its use for data analysis as well as in simulations and theory. We also show concretely the connections between the dimensionless units and experimental quantities. This work is funded in part by NSF grant DMR 06-06006 (Metals Program).

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