Intrinsic emergence of Majorana modes in Luttinger j=3/2 systems

TL;DR

This paper theoretically demonstrates that Majorana bound states can emerge in s-wave superconducting proximitized Luttinger j=3/2 systems, with topological phases induced by magnetic fields in one- and two-dimensional setups.

Contribution

It introduces two novel setups in Luttinger materials where Majorana modes can be realized, highlighting the role of band hybridization and magnetic fields without requiring Rashba coupling.

Findings

Two topological phase transitions at finite magnetic fields in 1D systems.

Topological regions in 2D Josephson junctions without BIA or Rashba coupling.

Majorana bound states can be realized in 2D Luttinger materials with magnetic field alone.

Abstract

We analyze theoretically two different setups for s-wave superconductivity (SC) proximitized $j=3/2$ particles in Luttinger materials that are able to host Majorana bound states (MBSs). First, we consider a one-dimensional SC wire with intrinsic bulk inversion asymmetry (BIA). In contrast to wires, modeled by a quadratic dispersion with Rashba spin-orbit coupling, there are two topological phase transitions in our systems at finite magnetic fields. Second, we analyze a two-dimensional Josephson junction on the Luttinger model finding a topological region even in the absence of BIA and Rashba spin-orbit couplings. This originates from the hybridization of the light and heavy hole bands of the $j=3/2$ states in combination with the SC pairing. As a consequence, both systems can be driven into a topological phase hosting MBSs. Hence, we predict that MBSs form in any SC proximitized Josephson junction on 2D Luttinger materials by the application of magnetic field alone. This opens a new avenue for the search of topological SC.