Topological properties are not protected in unstable crystal structures

The ability of DFT to reveal the consequences of assumed crystal symmetries on band inversion, band crossing and degeneracy in solids has led to a plethora of predicted compounds that should be topological insulators(TI’s), Dirac Semimetals(DSM) and unconventional quasiparticles. Before offering predicted compounds for experimental evaluation, it may be wise to use not only the band structures as design filters, but also the DFT total energy (E_tot) of the given crystal. Inspecting E_tot one finds: i) the predicted 3D non-symmorphic DSM band crossing of BiO₂ in assumed SiO₂ structure is dynamically unstable and disappears if its structure is allowed to relax to another polymorph;ii) the predicted 8-fold band degeneracy of CuBi₂O₄ in assumed nonmagnetic configuration disappears once energy-lowering spin polarization is allowed; iii) the predicted oxide TI BaBiO₃ with upshifted Fermi level disappears once allowed to lower its energy in response to n-type doping; iv) the predicted unconventional quasiparticle in Ba₄Bi₃ with downshifted Fermi energy is destabilized by the required p-type doping. Thus, although proven bulk topological characteristics lead to protected surface/edge states, nothing protects bulk states from thermodynamic instability.