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We study possible applications of high critical temperature nodalsuperconductors for the search for Majorana bound states in the DIII class. Wepropose a microscopic analysis of the proximity effect induced by d-wavesuperconductors on a semiconductor wire with strong spin-orbit coupling. Wecharacterize the induced superconductivity on the wire employing a numericalself-consistent tight-binding Bogoliubov-de Gennes approach, and analyticalconsiderations on the Green's function. The order parameter induced on thewire, the pair correlation function, and the renormalization of the Fermipoints are analyzed in detail, as well as the topological phase diagram in thecase of weak coupling. We highlight optimal Hamiltonian parameters to accessthe nontrivial topological phase which could display time-reversal invariantMajorana doublets at the boundaries of the wire.

High critical temperature nodal superconductors as building block for time-reversal invariant topological superconductivity