Electronic Structure Theory for Dark Matter Detection I

The hypothesized dilaton dark matter may cause the fine structure constant and other fundamental constants to vary. So far, experiments have not detected variation in the fine structure constant based on monitoring atomic transitions. However, the wavelengths are typically detected via silicon gratings, whose size may also vary with the fine structure constant. The purpose of this study is to investigate the influence of variation of the fine structure constant on the lattice constant and thermal expansion of crystalline silicon. This calculation was done with Density Functional Theory (DFT) in the real-space code Octopus. We vary the fine structure constant by tuning the strength of scalar and spin-orbit relativistic effects, affecting core electrons through the pseudopotentials generated in APE and valence electrons through the spin-orbit strength parameter in Octopus. We find a lattice constant variation of ~0.03% for changes between zero and full relativistic effects, dominated by core-core scalar relativistic effects. These results indicate a new experimental signature of fine structure variation and an effect that should be included in spectroscopic studies searching for the effects of dark matter.