‘Pseudo Majorana’ Modes in Clean Planar Josephson Junctions*

The unambiguous detection of Majorana bound states is essential for the study of such exotic states. In the presence of disorder, even theoretically, it is challenging to identify reliably the topological phase of the superconducting system and the presence of Majorana states. For quasi one-dimensional superconducting nanowires it has been proposed that the separation length of low energy modes can be used to assess the nature of such modes: low energy modes with a separation length comparable to the length of the nanowire can be identified as Majorana bound states. In this talk I will present results for planar Josephson junctions, a promising platform to realize Majorana bound states. We focus on the clean limit and find that very low energy modes, with large separation length, can be present even when the Josephson junction is known to be in a topologically trivial phase. I will then discuss the mechanism that can lead to the formation of such “pseudo-Majorana” states.