Fig. 1. (a) and (b) Top- and side-view of the bilayer α and δ phases, respectively. (c)–(f) Top- and side-views of monolayer Te in γ, β, ε, and ζ phases, respectively. Orange, red, and blue balls represent Te atoms in different sublayers along the interlayer direction z. (g)–(h) Total energies per Te atom and surface energies per unit area in different phases as a function of number of sublayers, respectively. The monolayer Te in α, γ, δ, ε, and ζ are presented with green, magenta, blue, orange, red, and black symbols, respectively.

Fig. 2. Structure evolution of ζ Te after layer stacking. (a) Bond lengths as a function of the number of sublayers. The blue and red lines correspond to intra- and average interlayer Te–Te bond lengths, respectively. (b) The evolution of layer heights in ζ few-layer with respect to sublayer number. The layers marked in red dotted rectangular frame tend to form a dimer or trimer when stacking together.

Fig. 3. Topological properties of tri-sublayer ζ Te. (a) The orbital projection of the tri-sublayer ζ without SOC. (b) The band structure of the tri-sublayer ζ with SOC. Red dashed rectangles mark the location of the band inversion and band opening with the SOC effect. The four time-reversal invariant points are labeled as Γ, X, Y and S. (c) The parities of filled states of tri-sublayer ζ at four time-reversal-invariant points in the Brillouin zone. The “+” and “–” correspond to even and odd parity, respectively. (d) Edge states of the ribbon ζ. Red and blue lines represent the ribbon and bulk states, respectively.

Fig. 4. Phase diagram of Te under charge doping. Relative total energy of mono- (a), bi- (b), and four-layer (c) Te in different phases as a function of electron/hole doping level. The total energies of the ζ phase were chosen as the energy reference. Lines with different colors correspond to the relative energies of different phases: α, black; β, red; γ, blue; δ, dark cyan; ε, magenta; ζ, dark gray.