The following describes content of the files in the archive (below, "(x)" stands for numerical part of the name of one of the files in the archive; figure numbers refer to figures in the accompanying publication): - Cut_9_64.mat - experimental ARPES map for Fig 2(a). - couplinggraphs.mat - plots in Fig 2(b). - Cut_9_06.mat - experimental ARPES map for Fig 3(a). - Cut_19.mat – experimental ARPES mao for Fig. 3(b). - (x)energyworkspace.mat - calculated ARPES maps for Fig 4 at energy (x). - experimental(x)workspace.mat - experimental data for Fig 4 at energy (x). - Bilayer_19_1.mat – original experimental ARPES data for twisted bilayer graphene in Fig 3 (b); workspace is organised in the same way as “E_contour_(x).mat” described below. - E_contour_(x).mat - original experimental ARPES data for twisted trilayer with twist angle (x); within this file, the structures "SMPM12058_(x)" contain information about photoelectrons with energy (x); the variables "x" and "y" correspond to kx and ky, respectively, and "value" to measured ARPES intensity; also contained within these structure is variable "info" which describes experimental details of the ARPES measurement. - IntensityCutTBLG134 and IntensityCutTBLG096 correspond to the supplementary figure 1, sub-figures (a) and (b) respectively.