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We consider a model for a one-dimensional quantum wire with Rashba spin-orbitcoupling and repulsive interactions, proximity coupled to a conventional s-wavesuperconductor. Using a combination of Hartree-Fock and density matrixrenormalization group calculations, we show that for sufficiently stronginteractions in the wire, a time-reversal invariant topological superconductingphase can be stabilized in the absence of an external magnetic field. Thisphase supports two zero-energy Majorana bound states at each end, which areprotected by time-reversal symmetry. The mechanism for the formation of thisphase is a reversal of the sign of the effective pair potential in the wire,due to the repulsive interactions. We calculate the differential conductanceinto the wire and its dependence on an applied magnetic field using thescattering-matrix formalism. The behavior of the zero-bias anomaly as afunction of the field direction can serve as a distinct experimental signatureof the topological phase.

Time-Reversal Invariant Topological Superconductivity Induced by Repulsive Interactions in Quantum Wires