Abstract
Ab-initio calculations show a pressure induced trivial-nontrivial-trivial topological phase transition in the normal state of 1T-TiSe2. The pressure range in which the nontrivial phase emerges overlaps with that of the superconducting ground state. Thus, topological superconductivity can be induced in protected surface states by the proximity effect of superconducting bulk states. This kind of self-induced topological surface superconductivity is promising for a realization of Majorana fermions due to the absence of lattice and chemical potential mismatches. For appropriate electron doping, the formation of the topological superconducting surface state in 1T-TiSe2 becomes accessible to experiments as it can be controlled by pressure.