  Edelstein effect is useful for electric control of magnetic moment. However,
Joule heating created by a dissipative current is harmful for its practical
applications. In this paper, we investigate two-dimensional noncentrosymmetric
superconductors (NCSs) with either $s$-wave or $d$-wave symmetry, and
demonstrate that a surface Edelstein effect is significantly enhanced in
$d$-wave NCSs. The origin of the enhancement is attributed to surface Majorana
states characteristic of gapless spin-singlet superconductors. In the view of
superconducting spintronics, this result would give a route to magnetic domain
switching by dissipationless supercurrent. We discuss a possible experimental
observation in cuprate superconductor heterostructures and heavy fermion
superlattices.
