We propose the use of three-dimensional Dirac materials as targets for direct detection of sub-MeV dark matter. Dirac materials are characterized by a linear dispersion for low-energy electronic excitations, with a small band gap of OðmeVÞ if lattice symmetries are broken. Dark matter at the keV scale carrying kinetic energy as small as a few meV can scatter and excite an electron across the gap. Alternatively, bosonic dark matter as light as a few meV can be absorbed by the electrons in the target. We develop the formalism for dark matter scattering and absorption in Dirac materials and calculate the experimental reach of these target materials. We find that Dirac materials can play a crucial role in detecting dark matter in the keV to MeV mass range that scatters with electrons via a kinetically mixed dark photon, as the dark photon does not develop an in-medium effective mass. The same target materials provide excellent sensitivity to absorption of light bosonic dark matter in the meV to hundreds of meV mass range, superior to all other existing proposals when the dark matter is a kinetically mixed dark photon.

We consider the direct detection of dark matter (DM) with polar materials, where single production of optical or acoustic phonons gives excellent reach to scattering of sub-MeV DM for both scalar and vector mediators.Using Density Functional Theory (DFT), we calculate the material-specific matrix elements, focusing on GaAs and sapphire, and show that DM scattering in an anisotropic crystal such as sapphire features a strong directional dependence. For example, for a DM candidate with mass 40 keV and relic abundance set by freeze-in, the daily modulation in the interaction rate can be established at 90% C.L. with a gram-year of exposure. Non-thermal dark photon DM in the meV -eV mass range can also be effectively absorbed in polar materials.

We show that the improper ferroelectric phase transition in the multiferroic hexagonal manganites displays appropriate symmetry-breaking characteristics for testing the Kibble-Zurek mechanism originally proposed to describe early-universe phase transitions. We present an analysis of the Kibble-Zurek theory of topological defect formation applied to the hexagonal manganites, discuss the conditions determining the range of cooling rates in which Kibble-Zurek behavior is expected, and show that recent literature data are consistent with our predictions. Finally, we explore experimentally the crossover out of the Kibble-Zurek regime and find a surprising reversal of the scaling behavior.