Majorana edge modes at topological insulator-superconductor-ferromagnet junctions in three dimensions

Recently the condition for the existence of gapless modes in arbitrary topological defects is proposed [Jeffrey C. Y. Teo and C. L. Kane, Phys. Rev. B 82, 115120 (2010)]. It is suggested that the existence of gapless modes follows from topologically nontrivial Hamiltonian which varies with adiabatic material-parameters characterizing the defects. We show that such adiabatic approach fails in cases of the existence of Majorana edge modes at topological insulator-superconductor-ferromagnet junctions. It is pointed out that quantum corrections beyond adiabatic quasiclassical approximation are required for the evaluation of second Chern number associated with the line junction.