Fig. 3: Unsupervised clustering by MSCA (multi-stage clustering algorithm) when the momentum space is divided into 200 cells.

a 200 normalized SSE (Sum of Squared Errors) curves obtained from first clustering, used as the input of the second clustering. b The SSE curve of the second clustering. c–e The second clustering results in momentum space for n = 2, 3, 4, respectively. The yellow region represents the inhomogeneous bands. The top band corresponds to the top valence band of MoS₂ at the Γ valley, while the bottom right corner shows a part of the BN band structure. h The iEDCs (angle-integrated energy distribution curves) obtained from the dataset belonging to the yellow region in Fig. 3d, used as the input of the third clustering. k The SSE curve of the third clustering. f, g The spatial distribution and 2D ARPES (angle-resolved photoemission spectroscopy) images of cluster 3-5 of n = 5 case. Different colors represent different phases. In Fig. 3f, the grey area labeled (1) corresponds to Au, the yellow area (2) to BN, the orange area (3) to MoS₂ on Au, the blue area (4) to monolayer MoS₂ on BN and the purple area (5) represents the combined signal from both sides of the edge. i, j The spatial distribution and 2D ARPES images of cluster 3-6 of n = 6 case. In Fig. 3i, the grey area labeled (1) corresponds to Au, the yellow area (2) to BN, the orange area (3) to MoS₂ on Au, the blue area (4) to monolayer MoS₂ on BN, the purple area (5) to multilayer MoS₂ on BN and the blue-violet area (6) represents the combined signal from both sides of the edge. l The 2D ARPES images of cluster 3-6 of n = 6 case in energy-angle range from E_k 94 to 96 eV and angle −5^∘ to 5^∘.