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In a superconducting topological insulator, superconducting vortex line maytrap 1-dimensional topological band with Majorana zero modes (MZMs) localizedat its ends. In this work, we study the effect of hexagonal warping to thevortex phase transition. We carry out both analytical calculations based on asemiclassical formula and numerical calculations based on full quantummechanics of Bogliubov de Gennes equation. We find that the hexagonal warpingterm enlarges the topological region of the vortex line as the chemicalpotential changes, and leads to the MZMs even in the absence of topologicalsurface states.

Hexagonal warping effect to Majorana zero modes at ends of superconducting vortex line in doped 3D strong topological insulators