Layer-by-layer disentanglement of Bloch states via frequency-domain photoemission

We report a layer-encoded frequency-domain ARPES experiment on a magnetic topological insulator (MnBi₂Te₄)(Bi₂Te₃) to characterize the layer origins of electronic states. Infrared laser excitations launch coherent lattice vibrations with the layer index encoded by the vibration frequency; photoemission spectroscopy tracks the electron dynamics, where the layer information is decoded in the frequency domain. This layer-frequency correspondence reveals a surprising wavefunction relocation of the topological surface state from the top magnetic layer into the buried second layer, reconciling the controversy over the vanishing broken-symmetry energy gap in (MnBi₂Te₄)(Bi₂Te₃) and its related compounds. The layer-frequency correspondence can be harnessed to disentangle electronic states layer-by-layer in a broad class of van der Waals superlattices.