Magnetisation control of the nematicity direction and nodal points in a superconducting doped topological insulator.

We study the effects of magnetisation on the properties of the doped topological insulator of the $\text{Bi}_2\text{Se}_3$ family with nematic superconductivity. We found that the direction of the in-plane magnetisation fixes the direction of the nematicity in the system. The chiral state is more favourable than the nematic state for large values of out-of-plane magnetisation. Overall, the critical temperature of the nematic superconductivity is robust against magnetisation. We explore in detail the spectrum of the system with the pinned direction of the nematic order parameter $\Delta_{y}$. Without magnetisation, there is a full gap in the spectrum because of finite hexagonal warping. At an out-of-plane $m_z$ or orthogonal in-plane $m_x$ magnetisation that is strong enough, the spectrum is closed at the nodal points that are split by the magnetisation. Flat Majorana surface states connect such split bulk nodal points. Parallel magnetisation $m_y$ lifts the nodal points and opens a full gap in the spectrum. We discuss relevant experiments and propose experimental verifications of our theory.