Effect of Fine Structure Constant on Lattice Constant and Thermal Expansion of Crystalline Silicon, as a Probe for Dark Matter*

The fine structure constant is one of the most fundamental constants of nature. It has no units and is equal to roughly 1/137. Dark matter theorists have hypothesized that dark matter may cause the fine structure constant to vary. So far experiment has found no variation in the fine structure constant based on atomic spectroscopy. The question has arisen whether the fine structure constant affects the size of the gratings through the lattice constant of the material. 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 computation was done with the code Octopus utilizing Density Functional Theory. We can vary the fine structure constant by tuning the strength of relativistic effects like spin-orbit coupling, both on the core and valence electrons. These results could reveal new experimental signatures of fine structure variation and provide information on other effects that should be included in spectroscopic studies searching for the effects of dark matter.