Topological states and topological phase transition in Cu_{2}SnS_{3} and Cu_{2}SnSe_{3}

Based on the first-principles calculations and model analysis, we propose that the isostructural compounds Cu_{2}SnS_{3} and Cu_{2}SnSe_{3} are both the simplest nodal-line semimetals with only one nodal line in their crystal momentum space when spin-orbit coupling (SOC) is ignored. The inclusion of SOC drives Cu_{2}SnS_{3} into a Weyl semimetal (WSM) state with only two pairs of Weyl nodes, the minimum number required for a WSM with time-reversal symmetry. In contrast, SOC leads Cu_{2}SnSe_{3} to a strong topological insulator (STI) state. This difference can be well understood as there is a topological phase transition (TPT). In it, the Weyl nodes are driven by tunable SOC and annihilate in a mirror plane, resulting in a STI. This TPT, together with the evolution of Weyl nodes, the changing of mirror Chern numbers of the mirror plane, and the Z_{2} indices protected by time-reversal symmetry, has been demonstrated by the calculation of Cu_{2}Sn(S_{1−x}Se_{x})_{3} within virtual crystal approximation and an effective k·p model analysis. Though our first-principles calculations have overestimated the topological states in both compounds, we believe that the theoretical demonstration of controlling the TPT and the evolution of Weyl nodes will stimulate further efforts to explore them.