Crystalline symmetry protected helical Majorana modes in the iron pnictides

We propose that propagating one-dimensional Majorana fermions will develop in the vortex cores of certain iron-based superconductors, most notably Li(Fe$_{1-x}$Co$_x$)As. A key ingredient of this proposal are the 3D Dirac cones recently observed in ARPES experiments [P. Zhang et al., Nat. Phys. $\textbf{15}$, 41 (2019)]. Using an effective Hamiltonian around the $\Gamma-Z$ line we demonstrate the development of gapless one-dimensional helical Majorana modes, protected by $C_4$ symmetry. A topological index is derived which links the helical Majorana modes to the presence of monopoles in the Berry curvature of the normal state. We present various experimental consequences of this theory and discuss its possible connections with cosmic strings.