Weyl semimetals from noncentrosymmetric topological insulators

We study the problem of phase transitions from 3D topological to normal insulators without inversion symmetry. In contrast with the conclusions of some previous work, we show that a Weyl semimetal always exists as an intermediate phase regardless of any constriant from lattice symmetries, although the interval of the critical region is sensitive to the choice of path in the parameter space and can be very narrow. We demonstrate this behavior by carrying out first-principles calculations on the noncentrosymmetric topological insulators LaBiTe$_3$ and LuBiTe$_3$ and the trivial insulator BiTeI. We find that a robust Weyl-semimetal phase exists in the solid solutions LaBi$_{1-x}$Sb$_x$Te$_3$ and LuBi$_{1-x}$Sb$_x$Te$_3$ for $x\!\approx\!38.5-41.9$\% and $x\!\approx\!40.5-45.1$\% respectively. A low-energy effective model is also constructed to describe the critical behavior in these two materials. In BiTeI, a Weyl semimetal also appears with applied pressure, but only within a very small pressure range, which may explain why it has not been experimentally observed.