Abstract
Because of their tiny band gaps Dirac materials promise to improve the sensitivity for dark matter particles in the sub-MeV mass range by many orders of magnitude. Here we study several candidate materials and calculate the expected rates for dark matter scattering via light and heavy dark photons as well as for dark photon absorption. A particular emphasis is placed on how to distinguish a dark matter signal from background by searching for the characteristic daily modulation of the signal, which arises from the directional sensitivity of anisotropic materials in combination with the rotation of the Earth. We revisit and improve previous calculations and propose two new candidate Dirac materials: BNQ-TTF and Yb$_3$PbO. We perform detailed calculations of the band structures of these materials and of ZrTe$_5$ based on density functional theory and determine the band gap, the Fermi velocities and the dielectric tensor. We show that in both ZrTe$_5$ and BNQ-TTF the amplitude of the daily modulation can be larger than 10% of the total rate, allowing to probe the preferred regions of parameter space even in the presence of sizeable backgrounds. BNQ-TTF is found to be particularly sensitive to small dark matter masses (below 100 keV for scattering and below 50 meV for absorption), while Yb$_3$PbO performs best for heavier particles.
Highlights
The realization that quantum materials, which have been the subject of great attention in recent years, may offer unique opportunities to search for light and very weakly interacting particles has led to a fruitful collaboration between particle physics and condensed matter physics
Detectors built from Dirac materials with sub-eV band gap are one of the most promising strategies to search for sub-MeV dark matter (DM) particles interacting with electrons via the exchange of a dark photon
II and III) we have revisited the formalism to calculate experimental event rates for the scattering or absorption of DM particles in anisotropic Dirac materials and have provided a number of improvements to previous results: (a) In Eq (2.18) we have introduced a simple way to include the anisotropy of the DM velocity distribution by calculating the velocity integral in terms of the minimum velocity vmin and the angle ψ between the momentum transfer and the velocity of Earth. (b) In Eq (2.21) we have proposed an improved way of defining the cutoff Λthat determines the region of reciprocal space where the electrons behave like a free Dirac fermion. (c) We have shown that in the case of dark photon absorption there is no daily modulation
Summary
The realization that quantum materials, which have been the subject of great attention in recent years, may offer unique opportunities to search for light and very weakly interacting particles has led to a fruitful collaboration between particle physics and condensed matter physics. There are at present no realistic estimates of the expected background level in a Dirac material and existing sensitivity studies in the literature are based on the assumption that backgrounds can be neglected This might be too optimistic since even in almost perfectly clean samples, states arising in tiny islands of impurity regions can lead to an exponentially small density of states in the mass gap of a Dirac semimetal [25,26]. [23] and reveal that one of the three materials mentioned in the study, the quasi-two-dimensional organic molecular crystal bis (naphthoquinone)-tetrathiafulvalene (BNQ-TTF), exhibits various Dirac crossings within the Brillouin zone when spin-orbit coupling is taken into account These nodes can potentially be gaped by applying stress and as a result breaking some of the crystalline symmetries protecting the Dirac nodes.
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