Topological aspects of π phase winding junctions in superconducting wires

Author： Spånslätt Christian Ardonne Eddy Hansson T H Spånslätt Christian

E-ISSN： 1361-648X|27|40|405701-405714

ISSN： 0953-8984

Source： Journal of Physics: Condensed Matter, Vol.27, Iss.40, 2015-10, pp. : 405701-405714

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Abstract

We theoretically investigate Josephson junctions with a phase shift of π in various proximity induced one-dimensional superconductor models. One of the salient experimental signatures of topological superconductors, namely the fractionalized &&dollar;4pi &dollar; ; 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 π-junctions coined ‘phase winding junctions’ where the phase of the order parameter rotates by an angle π 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 π-junctions. This effective theory is a one-dimensional version of similar theories describing Majorana bound states in half-vortices of two-dimensional topological superconductors.