Adiabatic manipulations of Majorana fermions in a three-dimensional network of quantum wires

Understand

It has been proposed that localized zero-energy Majorana states can be realized in a two-dimensional network of quasi-one-dimensional semiconductor wires that are proximity-coupled to a bulk superconductor.

• The wires should have strong spin-orbit coupling with appropriate symmetry, and their electrons should be partially polarized by a strong Zeeman field.
• Then, if the Fermi level is in an appropriate range, the wire can be in a topological superconducting phase, with Majorana states that occur at wire ends and at $Y$ junctions, where three topological superconductor segments may be joined.
• Here we generalize these ideas to consider a three-dimensional network.