Topological phase transitions in Sb(111) films driven by external strain and electric field

Using the first-principles calculations, we systematically study the lattice structure and topological phase transitions driven by external strain and electric field in Sb(111) thin films. The results show that 1-bilayer film is a robust trivial semiconductor, and the band gap of a 4-bilayer film can be tuned by strain but without gap closing up to strains of 8%, indicating a robust two-dimensional topological insulator. However, for the remaining bilayers below 9 bilayers, the topological phase transitions are driven if a suitable value of strain is applied. Moreover, the electric field not only can induce the Rashba splitting, but also may induce the gap closing at other points rather than at time-reversal invariant momenta. Our theoretical results provide efficient methods to manipulate topological phase transitions of Sb films.