How do we find dark matter on Earth?
The best evidence we have for dark matter is from large-scale gravitational and cosmological measurements. Combining these with precise measurements of the movement of stars near the sun, we infer that there must be dark matter right here in the vicinity of the Earth! Not a lot of it: the mass equivalent of one hydrogen atom per 3 cubic centimeters, which is slightly less dense than the near-vacuum of space. But it raises the exciting possibility of direct detection of dark matter: observing astrophysical dark matter using measurements taken on Earth.
One standard technique is to bury a giant tank of stuff (for example, silicon, germanium, or liquid xenon) deep underground and wait for a dark matter particle to bump into one of the constituent atoms. For dark matter heavier than a GeV, scattering off atomic nuclei provides the best signal, but for MeV-scale dark matter, the nucleus doesn't recoil enough to deposit significant energy (think of a ping-pong ball hitting a bowling ball). For this lighter dark matter, atomic electrons are a better target. With colleagues at Princeton and Berkeley, I recently proposed that the electrons in graphene (a 1-atom thick lattice of carbon atoms) could make an excellent dark matter detector. Just like in the photoelectric effect, where an incident photon can eject electrons from a surface, dark matter colliding with the graphene layer can eject an electron, whose energy and momentum we can measure. The lattice structure of graphene gives interesting angular correlations in the scattered electron momentum, very similar to the way X-ray diffraction gives information about the crystal structure of a material. In our case, we want to use "dark matter diffraction" to gain information about the dark matter mass and velocity distribution using the known properties of graphene.
The details of the scattering process, whether off nuclei or electrons, depend very sensitively on the velocity of the incoming dark matter particles. Faster particles have more kinetic energy, and can thus impart more energy to the target. But we have no direct evidence thus far for the velocity distribution of dark matter. All we know is that it must be described by some probability distribution, which must be positive-definite and normalized. It turns out that this information is enough to develop powerful "halo-independent" methods to compare the results of two experiments and see if they are consistent or not, independent of the particular form of the velocity distribution. I helped develop halo-independent analysis methods for unbinned data, useful in the early stages of dark matter detection if only a few events are observed, as well as a neat change of variables which allows the presentation of direct-detection results without making assumptions about the dark matter mass.