Monkhorst-Pack 𝐤-point sampling meshes listed in Table . These parameters were determined to converge the total energy to < 1 meV atom -1 and the pressure to < 1 kbar (0.1 GPa). The Materials Project has two entries for R3 ̅ m Bi2Te3, the second of which has a different ordering of the atoms within the quintuple layers, and which we denote R3 ̅ m*. The PBEsol GGA functional with the DFT-D3 dispersion correction (i.e. PBEsol+D3) was used to model exchange and correlation effects. PAW pseudopotentials were used to model the core electrons, with the valence electrons of S, Se, and Te and the valence and semi-core d electrons of Bi treated as valence states. Tolerances of 10 -8 eV and 10 -2 eV Å -1 were applied to total energy and forces during wavefunction and geometry optimisation, respectively. The size of the charge-density grids was set automatically to avoid aliasing errors, the PAW projections were performed in reciprocal space, and non-spherical contributions to the gradient corrections inside the PAW spheres were accounted for.