Chiral current-phase relation of topological Josephson junctions: A signature of the $4\pi$-periodic Josephson effect

Abstract

The $4\pi$-periodic Josephson effect is an indicator of Majorana zero modes and a ground-state degeneracy which are central to topological quantum computation. However, the observability of a $4\pi$-periodic Josephson current-phase relation (CPR) is hindered by the necessity to fix the fermionic parity. As an alternative to a $4\pi$-periodic CPR, this paper proposes a chiral CPR for the $4\pi$-periodic Josephson effect. This is a CPR of the form $J(\varphi )\propto C|\sin (\varphi /2)|$, describing a unidirectional supercurrent with the chirality $C=\pm 1$. Its non-analytic dependence on the Josephson phase difference $\varphi$ translates into the $4\pi$-periodic CPR $J(\varphi )\propto \sin (\varphi /2)$. The proposal requires a spin-polarized topological Josephson junction which is modeled here as a short link between spin-split superconducting channels at the edge of a two-dimensional topological insulator. In this case, $C$ coincides with the Chern number of the occupied spin band of the topological insulator. The paper details three scenarios of achieving a chiral CPR: By only Zeeman-like splitting, by Zeeman splitting combined with bias currents, and by an external out-of-plane magnetic field.

8 pages, 4 figures, published version

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Cited by in corpus (4)

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• Superconducting Diode Effect in Quantum Spin Hall Insulator-based Josephson Junctions
• Current-phase relation of a short multi-mode Bi2Se3 topological insulator nanoribbon Josephson junction with ballistic transport modes