  Future multi-tonne Direct Detection experiments will be sensitive to solar
neutrino induced nuclear recoils which form an irreducible background to light
Dark Matter searches. Indeed for masses around 6 GeV the spectra of neutrinos
and Dark Matter are so similar that experiments will run into a neutrino floor,
for which sensitivity increases only marginally with exposure past a certain
cross section. In this work we show that this floor can be overcome using the
different annual modulation expected from solar neutrinos and Dark Matter.
Specifically for cross sections below the neutrino floor the DM signal is
observable through a phase shift and a smaller amplitude for the time-dependent
event rate. This allows the exclusion power to be improved by up to an order of
magnitude for large exposures. In addition we demonstrate that the neutrino
floor exists over a wider mass range than has been previously shown, since the
large uncertainties in the Dark Matter velocity distribution make the signal
spectrum harder to distinguish from the neutrino background. However for most
velocity distributions the neutrino floor can still be surpassed using timing
information, though certain velocity streams may prove problematic.
