The study of hydrogen adsorption-induced topological surface state in-out hop in MgB₂ nodal-line semimetals via...

Hydrogen adsorption critically modulates topological surface states (TSSs) in the nodal-line semimetal MgB₂. We identify a threshold adsorption distance of 2.212 Å between H and surface B atoms, triggering an abrupt relocation of TSSs from inside to outside nodal-lines, referred to as "in-out hop." Beyond this distance, H weakly hybridizes with TSSs; subcritical adsorption induces the mutation of TSSs via covalent interactions. To resolve this phenomenon with quantum accuracy and data efficiency, we develop physics-informed Bayesian optimization (PIBO). PIBO unifies Dirac-derived constraints (TSSs' non-negativity and energy monotonicity) with sparse ab initio data, training a distance-dependent two-body model. With only 43 training points, PIBO achieves meV-level TSS reconstruction and establishes E_1+θ as an effective energy descriptor for coupled bands. This framework bypasses many-body intractability by embedding physical boundaries into ML workflows, enabling predictive engineering of adsorption-tuned topological devices. The PIBO methodology bridges ab initio precision and computational efficiency for accelerated quantum materials design.