  In a superconducting topological insulator, superconducting vortex line may
trap 1-dimensional topological band with Majorana zero modes (MZMs) localized
at its ends. In this work, we study the effect of hexagonal warping to the
vortex phase transition. We carry out both analytical calculations based on a
semiclassical formula and numerical calculations based on full quantum
mechanics of Bogliubov de Gennes equation. We find that the hexagonal warping
term enlarges the topological region of the vortex line as the chemical
potential changes, and leads to the MZMs even in the absence of topological
surface states.
