We theoretically investigate Josephson junctions with a phase shift of pi in various proximity induced one-dimensional superconductor models. One of the salient experimental signatures of topological superconductors, namely the fractionalized 4 pi periodic Josephson effect, is closely related to the occurrence of a characteristic zero energy bound state in such junctions. We make a detailed analysis of a more general type of pi-junctions coined 'phase winding junctions' where the phase of the order parameter rotates by an angle pi while its absolute value is kept finite. Such junctions have different properties, also from a topological viewpoint, and there are no protected zero energy modes. We compare the phenomenology of such junctions in topological (p-wave) and trivial (s-wave) superconducting wires, and briefly discuss possible experimental probes. Furthermore, we propose a topological field theory that gives a minimal description of a wire with defects corresponding to p-junctions. This effective theory is a one-dimensional version of similar theories describing Majorana bound states in half-vortices of two-dimensional topological superconductors.

We investigate the sub gap properties of a three terminal Josephson T-junction composed of topologically superconducting wires connected by a normal metal region. This system naturally hosts zero energy Andreev bound states which are of self-conjugate Majorana nature and we show that they are, in contrast to ordinary Majorana zero modes, spatially extended in the normal metal region. If the T-junction respects time-reversal symmetry, we show that a zero mode is distributed only in two out of three arms in the junction and tuning the superconducting phases allows for transfer of the mode between the junction arms. We further provide tunneling conductance calculations showing that these features can be detected in experiments. Our findings suggest an experimental platform for studying the nature of spatially extended Majorana zero modes.