Band-structure engineering of the magnetically Cr-doped topological insulator Sb₂Te₃ under mechanical strain

Magnetic doping in topological insulator Sb₂Te₃ can produce very novel physical phenomena such as quantum anomalous Hall effect (QAHE). However, experimental observations of QAHE in the magnetic atoms doped Sb₂Te₃ have encountered significant challenges due to the complexity of the electronic structure and the relatively small band gap. Generally, mechanical strain can effectively modulate the band structure, thus we theoretically investigate the electronic structures of Cr-doped Sb₂Te₃ under mechanical strain using first-principles calculations within density functional theory. The band gap of Cr-doped Sb₂Te₃ is 0.031 eV. When the compressive strain η becomes as  -2%, the band gap will be further enlarged to 0.045 eV, which is 45% larger than that of the unstrained material. However, as the compressive strain η exceed  -2%, strong hybridization between Cr and Te atoms will cause the overlap of bands, which leads to the closure of band gap. In addition, when tensile strain is applied to Cr-doped Sb₂Te₃, the decrease in the spacing between quintuple layers can enhance the coupling between Te and Sb atoms, which can also result in the closing of the band gap. Finally, we used HSE06 to calculated the band gaps. The band gaps may be underestimated, but HSE06 and GGA have the same band structures evolution tendency under mechanical strain. Our calculated results provide a guideline for the modulation of band structure by mechanical strain, which pave the way for the observation of QAHE in Cr-doped Sb₂Te₃.