Phonon-induced rotation of the electronic nematic director in superconducting doped Bi₂Se₃

Nematic superconductivity has been directly observed in the doped topological insulator A_xBi₂Se₃, with A={Cu, Nb, Sr}, as manifested by a two-fold symmetric in-plane critical field H_c2. The orientation of the elliptically-shaped in-plane H_c2 is set by the electronic nematic director, which is parametrized by an angle α. Since the nematic order parameter follows the Z₃-Potts model, the angle α naturally aligns with one of the three high-symmetry directions of the trigonal lattice of Bi₂Se₃. We find that the inclusion of acoustic phonons changes this phenomenology in a fundamental way in trigonal systems, but not in hexagonal ones. Trigonal systems have an additional elastic constant c₁₄, stemming from the fact that the in-plane and out-of-plane shear strain doublets belong to the same irreducible representation. We show that, when c₁₄ is large enough, the contribution to the nematic action coming from the coupling to the acoustic phonons makes the nematic director unlock from the high-symmetry directions. We discuss the implication of this rotation of the nematic director in H_c2 measurements, as well as the applicability of these results to doped Bi₂Se₃.