Tunable topological phase transition from nodal-line semimetal to Weyl semimetal by breaking symmetry

In this paper, we theoretically study the topological phase transition from nodal-line semimetal to Weyl semimetal. The nodal-line structure is protected by mirror symmetry and located on the ${k}_{x}\text{\ensuremath{-}}{k}_{y}$ mirror reflection plane, and the Hamiltonian of nodal-line semimetal has an emergent chiral symmetry on this plane. When the mirror symmetry is broken, the topological nodal line opens the gap and the nodal-line semimetal transition to Weyl semimetal with Weyl points on the ${k}_{x}$ axis or the ${k}_{y}$ axis. In addition, we break the chiral symmetry and realize the Weyl semimetal with the Weyl points on the ${k}_{z}$ axis. Destruction of the chiral symmetry leads to the gradual bending of the energy bands. With the evolution of the energy bands, the type-II nodal-line semimetal, the type-II Weyl semimetal and the type-I Weyl semimetal are successively realized. Furthermore, we also study the surface states of the nodal-line semimetal and the corresponding Weyl semimetals after the phase transition. Our work provides more ways to study the phase transition between nodal-line semimetal and Weyl semimetal and helps realize possible applications in topological electronic devices in the future.