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KZnSb crystallizes in the hexagonal P-6m2 space group. The structure is three-dimensional. K1+ is bonded in a 6-coordinate geometry to six equivalent Sb3- atoms. All K–Sb bond lengths are 3.79 Å. Zn2+ is bonded in a trigonal planar geometry to three equivalent Sb3- atoms. All Zn–Sb bond lengths are 2.64 Å. Sb3- is bonded in a distorted trigonal planar geometry to six equivalent K1+ and three equivalent Zn2+ atoms.
KZnSb crystallizes in the hexagonal P6_3/mmc space group. The structure is three-dimensional. K1+ is bonded to six equivalent Sb3- atoms to form a mixture of distorted edge, face, and corner-sharing KSb6 octahedra. The corner-sharing octahedral tilt angles are 41°. All K–Sb bond lengths are 3.77 Å. Zn2+ is bonded in a trigonal planar geometry to three equivalent Sb3- atoms. All Zn–Sb bond lengths are 2.64 Å. Sb3- is bonded in a distorted trigonal planar geometry to six equivalent K1+ and three equivalent Zn2+ atoms.
Alloy engineering is a well-established approach to tune various materials’ properties, but its application to topological alloys remains rudimentary. Of special interest is the band gap, the most defining property of topological materials; however, the concentration dependence of energy gaps in topological alloys remains unknown. Here we systematically investigate the band gap evolution of a topological alloy as a function of alloy concentration, using KZnSb 1-x Bi x as a prototype, based on first-principles calculations. In contrast to the well-established smooth bowing curve for a trivial gap in semiconductor alloys, we found that the topological gap evolves generally with a complex fragmented pattern due to topological phase transitions, and most strikingly a linear dependence on concentration locally in each distinct phase. Such gap linearization is fundamentally rooted in the linear dependence on alloy concentration of spin-orbit coupling (SOC) that predominantly determines a topological gap. Furthermore, we demonstrate topological alloy engineering as a general approach to tune the topological order by modulating the band edge composition and degeneracy through the alloying-induced interplay of SOC and atomic orbital on-site energy, while the linear gap dependence on alloy concentration remains independent of the degree of topological order.