Dirac and Weyl Semimetals in Sn1-xInxTe

SnTe is a well-characterized topological crystalline insulator material with an inverted bandgap at the L point in the fcc Brillouin zone, whereas Sn1-xInxTe is a superconductor. By utilizing first-principles and topological invariant calculations, we find distinct topological phase transitions in Sn1-xInxTe as a function of In content and crystal symmetry. For low In content, the inverted bandgap is maintained and the nontrivial insulator phase is unaffected. For In contentx >= 0.12, one of the bands is reverted, maintaining an odd number of inverted bands. The reverted band connects valence and conduction bands, forming a Dirac-like crossing close to the Fermi level, protected by crystal symmetry. Breaking of the inversion symmetry splits the fourfold degenerate Dirac crossing into pairs of Weyl nodes with opposite chirality. It is shown that this symmetry breaking can be performed by a ferroelectric effect, or by a Jahn-Teller distortion leading to a Weyl scenario. A phase diagram is predicted as a function of In content and the crystal symmetry, with topological crystalline insulator, Dirac and Weyl semimetal phases. The findings show that topological insulators can be used to realize a rich variety of fermions, especially when doping can induce reversion of inverted bands.