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

Abstract: Layer-by-layer material engineering has enabled exotic quantum phenomena such as interfacial superconductivity and the quantum anomalous Hall effect. Meanwhile, deciphering electronic states layer-by-layer remains a fundamental scientific challenge. This is exemplified by the difficulty in understanding the layer origins of topological electronic states in magnetic topological insulators, which is key to understanding and controlling topological quantum phases. Here, 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.