  We calculate for the first time the phonon excitation rate in the outer crust
of a neutron star due to scattering from light dark matter (LDM) particles
gravitationally boosted into the star. We consider dark matter particles in the
sub-GeV mass range scattering off a periodic array of nuclei through an
effective scalar-vector interaction with nucleons. We find that LDM effects
cause a modification of the net number of phonons in the lattice as compared to
the standard thermal result. In addition, we estimate the contribution of LDM
to the ion-ion thermal conductivity in the outer crust and find that it can be
significantly enhanced at large densities. Our results imply that for
magnetized neutron stars the LDM-enhanced global conductivity in the outer
crust will tend to reduce the anisotropic heat conduction between perpendicular
and parallel directions to the magnetic field.
