Figure 3.

Schematic illustration of the impact of the spin-orbit interaction induced band overlap in the Bi₂Te_3−xSe_x alloy system. The band extrema relevant for transport all exist within the bisectrix plane of the Brillouin zone (a). Two important locations within this plane are not indicated due to their position shifting slightly with alloy composition. The f point lies slightly offset from the ZF line, while the z lies along ΓZ. A simplified view of the effect of increasing the spin-orbit interaction is shown in (b). The gap of a typical semiconductor between cation conduction band states and anion valence band states closes with increasing spin-orbit interaction until the bands overlap. Due to the opposite parity of these specific bands in Bi₂Se₃ and Bi₂Te₃, an anticrossing occurs at the overlap creating a band gap and change of character for states at Γ. In Bi₂Te₃, the inversion is significant enough to invert the curvature at Γ and shifts the CBM towards a higher degeneracy point. Away from Γ, the energy level of other extrema shifts as shown by electronic structure calculations in (c–f) for Bi₂Se₃ with varying strengths of spin-orbit interaction. Doubling the strength of the interaction causes the CB extremum at Γ to shift to z and slightly above a sixfold valley at f, strongly resembling the calculated structure for Bi₂Te₃ (Figure 4).