  The usual Berry phase for a Majorana zero-energy state is zero. In this
manuscript, we propose a generalized geometric phase for Majorana zero-energy
state, which is non-zero for the electron or hole, respectively. We calculate
these non-zero geometric phases in a Ferromagnet (FI)/Topological Insulator
(TI)/Superconductor (SC) hybrid system, whose magnetization can be manipulated
by changing adiabatically the spin degree of freedom. The non-zero geometric
phases have potential application on the topological quantum computation
treatment of Majorana zero-energy modes. We also discuss the non-adiabatic
geometric phase associated with Majorana zero-energy state by the path integral
method.
