Layer-by-layer disentanglement of Bloch states

Layer-by-layer material engineering has produced interesting quantum phenomena such as interfacial superconductivity and the quantum anomalous Hall effect. However, probing electronic states layer by layer remains challenging. This is exemplified by the difficulty in understanding the layer origins of topological electronic states in magnetic topological insulators. Here we report a layer-encoded frequency-domain photoemission experiment on the magnetic topological insulator (MnBi₂Te₄)(Bi₂Te₃) that characterizes the origins of its electronic states. Infrared laser excitations launch coherent lattice vibrations with the layer index encoded by the vibration frequency. Photoemission spectroscopy then tracks the electron dynamics, where the layer information is carried in the frequency domain. This layer–frequency correspondence shows 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.