Abstract
We propose a new setup for creating Majorana bound states in a two-dimensional electron gas Josephson junction. Our proposal relies exclusively on a supercurrent parallel to the junction as a mechanism of breaking time-reversal symmetry. We show that combined with spin-orbit coupling, supercurrents induce a Zeeman-like spin splitting. Further, we identify a new conserved quantity—charge-momentum parity—that prevents the opening of the topological gap by the supercurrent in a straight Josephson junction. We propose breaking this conservation law by adding a third superconductor, introducing a periodic potential, or making the junction zigzag-shaped. By comparing the topological phase diagrams and practical limitations of these systems we identify the zigzag-shaped junction as the most promising option.
Highlights
Majorana bound states (MBS) are a promising avenue for fault tolerant quantum computation due to their topological protection [1,2,3,4]
In order to check how robust the resulting topological superconductivity is, we study the topological phase diagrams of the three candidate systems as a function of λ and μ, focusing especially on the effect of winding of the superconducting phase becoming incommensurate with the other periods appearing in the Hamiltonian: λV and zx
We have shown that the winding of a superconducting phase is a sufficient source of time-reversal symmetry breaking to create MBS in Josephson junctions
Summary
Majorana bound states (MBS) are a promising avenue for fault tolerant quantum computation due to their topological protection [1,2,3,4]. The most commonly used scheme relies on the Zeeman effect created by an external magnetic field in a proximitized semiconducting nanowire [14,15,16,17,18,19,20,21] This approach requires strong magnetic fields because the electron spin splitting must exceed the induced superconducting gap in the topological phase. Making the superconducting phase depend only y coordinate coordinate is insufficient, because at kx = 0 the spin-orbit coupling may be removed by a transformation ψ( y) → exp[iσx f ( y)]ψ( y), and all states are doubly degenerate The source code and data used to produce the figures in this work are available in Ref. [39]
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