Narayan Mohanta

Demonstration of non-Abelian statistics of Majorana bound states (MBS) is crucial for the realization of fault-tolerant topological quantum computation. Two-dimensional platforms such as planar Josephson junction (PJJ) require an in-plane magnetic field to generate a pair of MBS at its non-superconducting channel ends; however, the fixed direction of the in-plane magnetic field puts a constraint on the realization of a multi-terminal topological planar junction, and hence its ability to physically move multiple MBS—which is necessary for performing the fusion and braiding operations. Here we show that in a PJJ coupled to a Skyrmion crystal, which can generate multiple pairs of MBS in the absence of any external magnetic field, the non-trivial fusion and braiding operations can be performed. Our numerical calculations, designed for realistic two-dimensional quantum systems, certify the feasibility of experimental realization of the proposed device schemes. We find that both s -wave and d -wave superconducting leads can generate the MBS; indicating that the MBS movement operations can be performed at higher temperatures using d -wave superconducting leads. Our results establish that the Skyrmion crystal-coupled PJJ is a viable platform for the generation and controlled movement of the MBS.

We propose an altermagnet-topological insulator bilayer as a platform to engineer Berry phase driven spin-charge responses using an interfacial buffer layer. Using a momentum-space lattice model and linear-response theory, we investigate a $d$-wave altermagnet coupled to a topological insulator and highlight the crucial role of spin-flip tunneling in shaping its electronic and transport properties. Interfacial hybridization strongly modifies the band structure, leading to anisotropic Rashba-Edelstein and Hall responses. The spin-flip component of the coupling induces an inverse $d$-wave spin texture in the altermagnetic bands, signaling the onset of an altermagnetic topological phase. This coupling also renders the Rashba-Edelstein effect strongly in-plane anisotropic, enhancing the transverse response relative to ferromagnetic or antiferromagnetic analogues. These results establish interfacial spin-flip tunneling as a practical control knob for direction-sensitive, stray-field-free spin-charge conversion in correlated topological heterostructures.