Current-phase relation for Josephson effect through helical metal

Abstract

Josephson junctions fabricated on the surface of three-dimensional topological insulators (TI) show a few unusual properties distinct from conventional Josephson junctions. In these devices, the Josephson coupling and the supercurrent are mediated by helical metal, the two-dimensional surface of the TI. A line junction of this kind is known to support Andreev bound states at zero energy for phase bias π, and consequently the so-called fractional ac Josephson effect. Motivated by recent experiments on TI-based Josephson junctions, here we describe a convenient algorithm to compute the bound state spectrum and the current-phase relation for junctions with finite length and width. We present analytical results for the bound state spectrum, and discuss the dependence of the current-phase relation on the length and width of the junction, the chemical potential of the helical metal, and temperature. A thorough understanding of the current-phase relation may help in designing topological superconducting qubits and manipulating Majorana fermions.

References in corpus (8)

• Superconducting proximity effect and Majorana fermions at the surface of a topological insulator
• Andreev reflection and Klein tunneling in graphene
• Specular Andreev reflection in graphene
• Bulk Band Gap and Surface State Conduction Observed in Voltage-Tuned Crystals of the Topological Insulator Bi${}_2$Se${}_3$
• Proximity effect at the superconductor - topological insulator interface
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• Nearly flat Andreev bound states in superconductor-topological insulator hybrid structures

Cited by in corpus (1)

• Spin-helical transport in normal and superconducting topological insulators