Majorana Braiding Racetracks from Charge Chern Insulator - Superconductor Hybrids

Recent experiments have provided evidence for chiral charge order in Kagome superconductors (SCs). This intriguing possibility motivates us to unveil the first pathway to engineer topological superconductivity by harnessing the interplay of charge Chern insulators (CIs) and conventional SCs. We here identify under which conditions a pyramidal SC/CI/SC heterostructure induces an effective 1D spinless p-wave SC that allows pinning Majorana zero modes (MZMs) at termination edges and domain walls. As we reveal, such a MZM track is controlled by the phase difference of the two SCs involved and additional magnetic fields which are required for generating Rashba-like spin-orbit coupling. Further, we show that a SC/CI/SC/CI/SC double-pyramidal hybrid defines a double MZM track, in which braiding occurs by varying the two superconducting phase differences in space and adiabatically in time. Given the geometry of the MZM racetrack, we propose to employ the time-averaged quadrupolar differential conductance to confirm the here-termed MZM track exchange process which is pivotal for braiding. In addition, we identify experimental knobs which enable the fusion of MZM pairs, and the detection of the underlying non-Abelian topological order and twofold many-body ground state degeneracy by encoding it in a topological invariant.