Josephson junction on one edge of a two dimensional topological insulator affected by magnetic impurity

Abstract

Current-phase relation in a Josephson junction formed by putting two s-wave superconductors on the same edge of a two dimensional topological insulator is investigated. We consider the case that the junction length is finite and magnetic impurity exists. The similarity and difference with conventional Josephson junction is discussed. The current is calculated in the semiconductor picture. Both the $2\pi$- and $4\pi$-period current-phase relations ($I_{2\pi }(\varphi ),I_{4\pi }(\varphi )$) are studied. There is a sharp jump at $\varphi =\pi$ and $\varphi =2\pi$ for $I_{2\pi }$ and $I_{4\pi }$ respectively in the clean junction. For $I_{2\pi }$, the sharp jump is robust against impurity strength and distribution. However for $I_{4\pi }$, the impurity makes the jump at $\varphi =2\pi$ smooth. The critical (maximum) current of $I_{2\pi }$ is given and we find it will be increased by asymmetrical distribution of impurity.

7 pages, 5 figures

References in corpus (10)

• Superconducting proximity effect and Majorana fermions at the surface of a topological insulator
• Majorana Fermions and a Topological Phase Transition in Semiconductor-Superconductor Heterostructures
• New directions in the pursuit of Majorana fermions in solid state systems
• The Helical Liquid and the Edge of Quantum Spin Hall Systems
• AC Josephson effect in finite-length nanowire junctions with Majorana modes
• Fermion-parity anomaly of the critical supercurrent in the quantum spin-Hall effect
• Non-equilibrium Josephson effect through helical edge states
• Phenomenology and Dynamics of Majorana Josephson Junction
• Mutation of Andreev into Majorana bound states in long NS and SNS junctions
• Josephson Current through a Semiconductor Nanowire: effect of strong spin-orbit coupling and Zeeman splitting

Cited by in corpus (9)

• Microwave signatures of Majorana states in a topological Josephson junction
• Revealing topological superconductivity in extended quantum spin Hall Josephson junctions
• Evidence for Majorana bound states in transport properties of hybrid structures based on helical liquids
• Screening Clouds and Majorana Fermions
• Design of Josephson diode based on magnetic impurity
• Switch effect and $0$-$\pi$ transition in Ising superconductor Josephson junctions
• Low-energy electronic properties of Weyl semimetal quantum dot
• Spin phase regulated spin Josephson supercurrent in topological superconductor
• Design of a Josephson diode based on double magnetic impurities