Geometric Josephson effects in chiral topological nanowires

Abstract

One of the salient signatures of Majorana zero modes and topological superconductivity is a $4\pi$-periodic Josephson effect due to the combination of fermion parity conservation and the presence of a topologically protected odd number of zero energy crossings in the Andreev spectrum. In this paper, we study this effect in Josephson junctions composed of two semiconducting nanowires with Rashba spin-orbit coupling and induced superconductivity from the proximity effect. For certain orientations of the external magnetic field, such junctions possess a chiral symmetry and we show how this symmetry allows the Andreev spectrum and the protected crossings to be shifted by introducing a relative angle between the two wires. The junction then displays a geometrically induced anomalous Josephson effect, the flow of a supercurrent in the absence of external phase bias. Furthermore, we derive a proportionality relation between the local current density and the local curvature for a single curved wire. This result can be viewed as a one-dimensional analogue of the recently proposed geo-Josephson effect [Kvorning et al., arXiv:1709.00482]. Our two proposed effects can in principle be used as signatures of topological superconductivity in one dimension.

arXiv comment7 pages, 3 figures

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• Tomography of zero-energy end modes in topological superconducting wires
• Topological superconducting phases and Josephson effect in curved time-reversal-invariant superconductors
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• Engineering Ponderomotive Potential for Realizing $\pi$ and $\pi /2$ Bosonic Josephson Junctions
• Antichiral edge states and Bogoliubov Fermi surfaces in a two-dimensional proximity-induced superconductor