  The cosmic ray flux at the lowest energies, $\lesssim 10$ GeV, is modulated
by the solar cycle, inducing a time variation that is expected to carry over
into the atmospheric neutrino flux at these energies. Here we estimate this
time variation of the atmospheric neutrino flux at five prospective underground
locations for multi-tonne scale dark matter detectors (CJPL, Kamioka, LNGS,
SNOlab and SURF). We find that between solar minimum and solar maximum, the
normalization of the flux changes by $\sim 30\%$ at a high-latitude location
such as SURF, while it changes by a smaller amount, $\lesssim 10\%$, at LNGS. A
dark matter detector that runs for a period extending through solar cycles will
be most effective at identifying this time variation. This opens the
possibility to distinguish such neutrino-induced nuclear recoils from dark
matter-induced nuclear recoils, thus allowing for the possibility of using
timing information to break through the "neutrino floor."
