Nuclear spin ordering and Majorana edge states in interacting one-dimensional systems

The interactions between the electrons of a one-dimensional conductor and its nuclear spins can lead to an ordered phase in which both degrees of freedom are tightly bound to each other. Experimentally available examples of such a system are GaAs-based quantum wires. In these systems the hyperfine interaction between the nuclear spin and the conduction electron spin is weak, yet it triggers a strong feedback reaction that results in an ordered phase consisting of a nuclear helimagnet that is inseparably bound to an electronic density wave combining charge and spin degrees of freedom. When this quantum wire is brought in proximity of s-wave superconductor, it supports Majorana edge states. We show that this Majorana edges states are extremely susceptible to electron-electron interactions. Strong interactions generically destroy the induced superconducting gap that stabilizes the Majorana edge states. For weak interactions, the renormalization of the gap is nonuniversal and allows for a regime, in which the Majorana edge states persist. We present strategies how this regime can be reached.

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