Topological aspects of $\pi$ phase winding junctions in superconducting wires

Abstract

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 $\pi$-junctions. This effective theory is a one-dimensional version of similar theories describing Majorana bound states in half-vortices of two-dimensional topological superconductors.

15 pages, 9 figures; v2: sections 3 and 4 streamlined

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Cited by in corpus (7)

• Theory of time reversal topological superconductivity in double Rashba wires -- symmetries of Cooper pair and Andreev bound states
• Distinguishing between Topological and Quasi Majorana Zero Modes with a Dissipative Resonant Level
• Geometric Josephson effects in chiral topological nanowires
• Synthesizing Majorana zero-energy modes in a periodically gated quantum wire
• Tuning Majorana zero modes with temperature in $\pi$-phase Josephson junctions
• One-dimensional ${\mathbb{Z}}_4$ topological superconductor
• On the Electromagnetic Response of Topological Superconductors