The topological insulator has an intriguing electronic structure in that it has nontrivial topology enforcing the helical Dirac fermionic states at interfaces to the band insulators. Protected by the time-reversal symmetry and finite band gaps in the bulk, the topology is immune to external nonmagnetic perturbations. One essential question is whether elementary excitations in solids like phonons can trigger a transition in the topological property of the electronic structures. Here we investigate the development of topological insulating phases in IV-VI compounds under dynamic lattice deformations using first-principles calculations. Unlike the static state of topological phases at equilibrium conditions, we show that nontrivial topological phases are induced in the compounds by the dynamic lattice deformations from selective phonon modes. Calculations of the time-reversal polarization show that the $Z_2$ invariant of the compounds is flipped by the selective phonon modes and that the compounds exhibit oscillating topological phases upon dynamic lattice deformations.

• Received 26 March 2015
• Revised 18 August 2015

DOI:https://doi.org/10.1103/PhysRevB.92.125142