Phonon-induced rotation of the electronic nematic director in superconducting <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msub><mml:mi>Bi</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:msub><mml:mi>Se</mml:mi><mml:mn>3</mml:mn></mml:msub></mml:mrow></mml:math>

The doped topological insulator ${A}_{x}{\mathrm{Bi}}_{2}{\mathrm{Se}}_{3}$, with $A={\mathrm{Cu},\mathrm{Sr},\mathrm{Nb}}$, becomes a nematic superconductor below ${T}_{c}\ensuremath{\approx}3$--4 K. associated electronic director is described by an angle $\ensuremath{\alpha}$ and experimentally manifested in the elliptical shape of in-plane critical magnetic field ${H}_{c2}$. Because threefold rotational symmetry lattice, expected to align one three high-symmetry directions corresponding nearest-neighbor bonds, consistent ${Z}_{3}$-Potts transition. Here, we show that coupling acoustic phonons, which makes correlation length tend diverge along certain only, can fundamentally alter this phenomenology trigonal lattices. Compared hexagonal lattices, former possesses sixth independent elastic constant ${c}_{14}$ due fact shear strain doublet $({\ensuremath{\epsilon}}_{xx}\ensuremath{-}{\ensuremath{\epsilon}}_{yy},\ensuremath{-}2{\ensuremath{\epsilon}}_{xy})$ out-of-plane $(2{\ensuremath{\epsilon}}_{yz},\ensuremath{-}2{\ensuremath{\epsilon}}_{zx})$ transform as same irreducible representation. We find that, when overcomes threshold value, be case ${\mathrm{Bi}}_{2}{\mathrm{Se}}_{3}$, unlocks from competition between quadratic phonon-mediated interaction cubic anharmonicity. This implies breaking residual twofold (${C}_{2x}$), resulting triclinic phase. discuss implications these findings for structure domains, ${H}_{c2}$ presence nodes inside superconducting state.