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We develop a formalism to describe electron ejections from graphene-liketargets by dark matter (DM) scattering for general forms of scalar and spin 1/2DM-electron interactions and compare their applicability and accuracy withinthe density functional theory (DFT) and tight binding (TB) approaches. Thisformalism allows for accurate prediction of the daily modulation signalexpected from DM in upcoming direct detection experiments employing graphenesheets as the target material. A key result is that the physics of the graphenesheet and that of the DM and the ejected electron factorise, allowing for therate of ejections from all forms of DM to be obtained with a single grapheneresponse function. We perform a comparison between the TB and DFT approaches tomodeling the initial state electronic wavefunction within this framework, withDFT emerging as the more self-consistent and reliable choice due to thechallenges in the embedding of an appropriate atomic contribution into the TBapproach.

Direct searches for general dark matter-electron interactions with graphene detectors: Part I. Electronic structure calculations