Topological Interface Engineering in Weyl–Superconductor Heterostructures: Emergent Majorana Arcs, Non-Abelian Braiding, and K-Theory Classification via the Stratum Model

Topological Interface Engineering in Weyl–Superconductor Heterostructures: Emergent Majorana Arcs, Non-Abelian Braiding, and K-Theory Classification via the Stratum Model Mehmet Keçeci Orcid: https://orcid.org/0000-0001-9937-9839 Abstract: In this study, a heterostructure consisting of topological insulator (TI), superconductor (SC), topological defect, and Weyl semimetal layers is investigated within the framework of the Stratum Model using a K-theory approach. For the TI layer, the Chern number is found to be C = −1 on the Qi–Wu–Zhang model via the Fukui–Hatsugai–Suzuki Berry curvature integral. In the SC layer, by solving the Kitaev chain, localized Majorana zero modes at the edges and the ℤ₂ = 1 invariant are verified. The defect layer is characterized by the winding number (deg = 1) of the 𝕋² → 𝕊² mapping. For the Weyl semimetal, in a two-band model, Weyl nodes with opposite chirality are obtained at kz = ±√m positions; the topological charge of this layer is determined as two Weyl points. At the Weyl–SC interface, the proximity effect is modeled with a Bogoliubov–de Gennes Hamiltonian including singlet s-wave pairing and a Zeeman field in the z-direction. The analytically derived condition |m − kz² + h| = |Δ| shows that Majorana arcs form in the range kz ≈ ±1.3038 for h = 1.0 and Δ = 0.3; this result is verified by numerical simulations. By constructing the phase diagram in the (h, Δ) plane, the region where the arcs are stable is mapped. The non-Abelian statistics of Majorana modes are simulated with the braiding operator U = exp(πγ₂γ₃/4) in the 4×4 representation of the Clifford algebra; the evolution of the initial state |00⟩ into the superposition (|00⟩ + i|11⟩)/√2 proves the change in fermion parity and the non-commutative nature of braiding. K-theory analysis shows that the mass invariants of each layer (for TI K⁰(𝕋²) = ℤ, for SC K⁰₋₂(pt) = ℤ₂, for the defect layer the winding number π₂(𝕊²)) remain well-defined under proximity interaction and provide a unified topological protection. These findings reveal that Weyl–superconductor heterostructures offer a suitable platform for realizing Majorana fermions and for topological quantum computation. Keywords: Topological insulator, Weyl semimetal, Majorana fermions, Non-Abelian braiding, K-theory, Stratum model, Bogoliubov–de Gennes Hamiltonian, BdG, Proximity effect, Majorana arcs, Topological quantum computation.