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Based on the first-principles calculations within local density approximationand model analysis, we propose that the iso-structural compounds Cu2SnS3 andCu2SnSe3 are both the simplest nodal line semimetals with only one nodal linein their crystal momentum space when spin-orbit coupling (SOC) is ignored. Theincluding of SOC drives Cu2SnS3 into a Weyl semimetal (WSM) state with only twopairs of Weyl nodes, the minimum number required for WSM with time reversalsymmetry. In contrast, SOC leads Cu2SnSe3 to strong topological insulator (TI)state. This difference can be well understood as there is a topological phasetransition (TPT). In it, the Weyl nodes are driven by tunable SOC andannihilate in a mirror plane, resulting in a TI. This TPT, together with theevolution of Weyl nodes, the changing of mirror Chern numbers of mirror planeand the Z2 indices protected by time-reversal symmetry has been demonstrated bythe calculation of Cu2SnS3-xSex within virtual crystal approximation and aneffective k $\cdot$ p model analysis. Though our first-principles calculationshave overestimated the topological states in both compounds, we believe thatthe theoretical demonstration of controlling TPT and evolution of Weyl nodeswill stimulate further efforts in exploring them.

Topological states and topological phase transition in Cu2SnS3 and Cu2SnSe3