A periodic lattice distortion that reduces the translational symmetry folds electron bands into a reduced Brillouin zone, leading to band mixing and a tendency to gap formation, as in the Peierls transition in one-dimensional systems. However, in higher dimensions, the resulting phase can present topological obstructions preventing a complete gap opening. We discuss two different mechanisms for such obstructions: emergent Weyl nodes and symmetry protected band crossings. Based on density-functional calculations, we show these mechanisms are at play in trigonal ${\mathrm{PtBi}}_2$.

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• Electronic structure
• First-principles calculations
• Spin-orbit coupling
• Topological materials
• Nodal-line semimetals
• Weyl semimetal
• Band structure methods
• Density functional theory
• Wannier function methods