  We study possible applications of high critical temperature nodal
superconductors for the search for Majorana bound states in the DIII class. We
propose a microscopic analysis of the proximity effect induced by d-wave
superconductors on a semiconductor wire with strong spin-orbit coupling. We
characterize the induced superconductivity on the wire employing a numerical
self-consistent tight-binding Bogoliubov-de Gennes approach, and analytical
considerations on the Green's function. The order parameter induced on the
wire, the pair correlation function, and the renormalization of the Fermi
points are analyzed in detail, as well as the topological phase diagram in the
case of weak coupling. We highlight optimal Hamiltonian parameters to access
the nontrivial topological phase which could display time-reversal invariant
Majorana doublets at the boundaries of the wire.
