# Magnetoelectrically-Tunable Andreev-Bound-State Spectra and Spin Polarization in P-Wave Josephson Junctions

## TL;DR

This paper explores how electrical gating can control the order parameter orientation in p-wave Josephson junctions, enabling manipulation of Majorana bound states, ABS spectra, and spin polarization for potential quantum computing applications.

## Contribution

It introduces a method to electrically control the d-vector orientation in p-wave superconductors, affecting MBSs and ABS spectra, with implications for topological quantum devices.

## Key findings

- Electrical gating switches d-vector orientation
- ABS spectra can be twisted by charge/spin-phase differences
- Distinct spin polarization patterns enable MBS detection

## Abstract

We demonstrate how the boundary-driven reconstruction of the superconducting order parameter can be employed to manipulate the zero-energy Majorana bound states (MBSs) occurring in a topological Josephson junction. We focus on an interface of two p-wave superconductors, which are described by a spin-vector order parameter $\bf{d}$. Apart from the sensitivity of $\bf{d}$ to external Zeeman/exchange fields, here, we show that the orientation of $\bf{d}$ throughout the junction can be controlled by electrically gating the weak link. The remarkable local character of this knob is a manifestation of the edge reconstruction of the order parameter, which takes place whenever different $\bf{d}$-vector configurations in each superconductor compete and are close in energy. As a consequence, the spin-dependent superconducting-phase difference across the junction is switchable from $0$ to $\pi$. Moreover, in the regime where multiple edge MBSs occur for each superconductor, the Andreev-bound-state (ABS) spectra can be twisted by the application of either a charge- or spin-phase difference across the interface, and give rise to a rich diversity of nonstandard ABS dispersions. Interestingly, some of these dispersions show band crossings protected by fermion parity, despite their $2\pi$-periodic character. These crossings additionally unlock the possibility of nontrivial topology in synthetic spaces, when considering networks of such 1D junctions. Lastly, the interface MBSs induce a distinct elecronic spin polarization near the junction, which possesses a characteristic spatial pattern that allows the detection of MBSs using spin-polarized scanning tunneling microscopy. These findings unveil novel paths to mechanisms for ABS engineering and single-out signatures relevant for the experimental detection and manipulation of MBSs.