Fig. 3

(a1–a6) Calculated band structure of a 12 SL thick slab of \(\textrm{Mn}_{1-x} \textrm{Ge}_x \textrm{Bi}_2 \textrm{Te}_4\) in the \(\bar{K}\!\bar{ \varGamma }\!\bar{M}\) direction in the BZ for Ge concentrations from 0% to 75%. Surface states are highlighted in light brown, and bulk states in black-blue-white. Horizontal dashed black lines indicate the energy positions of TrSS at the \(\bar{\Gamma }\) point. Horizontal solid red lines indicate the TSS positions, which are present for Ge concentrations up to 33%. (b1–b6) and (c1–c6) depict the bulk and surface band structures, respectively, using a Lorentzian smearing of 30 meV FWHM. Each image contains EDCs taken at the \(\bar{\Gamma }\) point (white curves). Horizontal white lines indicate the energy positions of EDC peak centers, while solid red horizontal lines show the TSS positions from figures (a1–a6).