  We show that a two-dimensional semiconductor with Rashba spin-orbit coupling
could be driven into the second-order topological superconducting phase when a
mixed-pairing state is introduced. The superconducting order we consider
involves only even-parity components and meanwhile breaks time-reversal
symmetry. As a result, each corner of a square-shaped Rashba semiconductor
would host one single Majorana zero mode in the second-order nontrivial phase.
Starting from edge physics, we are able to determine the phase boundaries
accurately. A simple criterion for the second-order phase is further
established, which concerns the relative position between Fermi surfaces and
nodal points of the superconducting order parameter. In the end, we propose two
setups that may bring this mixed-pairing state into the Rashba semiconductor,
followed by a brief discussion on the experimental feasibility of the two
platforms.
