Fig. 2: Theoretical atomic and electronic structures of the coloring-triangle latticed MoTe₂ (CT-MoTe₂) phase.

a Illustration of the triangular lattice of the smallest MTTDs (highlighted by red dashed triangles) inside the associated MTB triangles (orange dotted triangles, hereinafter), which are arranged in a corner-to-edge manner. The black dashed rhombus indicates the supercell of the lattice (hereinafter). b Illustration of the hexagonal lattice of the smallest MTTDs (highlighted by blue triangles) among the associated MTBs, connected in a corner-to-corner manner. The central Te atoms in MTTDs are highlighted by the red (Te_MTTD-R) and blue (Te_MTTD-B) circles, respectively. c Schematic of the formed coloring-triangle (CT) lattice of CT-MoTe₂, composed of both triangular (a) and hexagonal (b) lattice of the smallest MTTDs. d Illustration of the atomic structure of the CT-MoTe₂ phase. e Theoretical band structures of the CT-MoTe₂ monolayer, varying colors denote different sets of kagome-like bands and their irreducible representations (irreps) were also denoted. f Corresponding total density of states (DOS) of the CT-MoTe₂ monolayer. Four bands of t-S0, t-S1, t-S2 and t-S3 are shown in the DOS, where t represents theoretical. g, h Zoomed-in band structures of two sets of the CT bands display in green lines (CT1) and blue lines (CT2). i–l 2D contour of visualized wavefunction norms at the K point (see blue rectangles in g and h) for CT1-A (i), CT1-B (j), CT2-A (k), and CT2-B (l), respectively. The isosurface values were kept fixed at 2 × 10⁻⁴ e Bohr⁻³.