Topological Classification of Correlated Heterostructures from Ab Initio Simulations

Determining Chern numbers is crucial for identifying and classifying topological phases in realistic materials. While first-principles methods for evaluating Chern numbers in electronic Hamiltonians are well established, their extension to Bogoliubov–de Gennes (BdG) Hamiltonians in multiband heterostructures remains a major challenge. We present a systematic framework for computing Chern numbers from Wannier-based Hamiltonians derived separately from ab initio theory. Starting with single-orbital BdG models, we establish robust numerical convergence criteria and then extend the approach to semiconductor–superconductor heterostructures. By constructing maximally localized Wannier functions, we downfold the electronic structure to a low-energy subspace that preserves orbital character, explicitly incorporating orbitally selective Rashba spin–orbit coupling and superconducting pairings. Chern numbers are evaluated from Matsubara Green's functions and their derivatives. This framework reveals how realistic multiband effects reshape topological behavior in heterostructures, offering predictive guidance for designing platforms capable of hosting robust topological phases.