  The success of photonic crystal fibres relies largely on the endless variety
of two-dimensional photonic crystals in the cross-section. Here, we propose a
topological bandgap fibre whose bandgaps along in-plane directions are opened
by generalized Kekul\'e modulation of a Dirac lattice with a vortex phase.
Then, the existence of mid-gap defect modes is guaranteed to guide light at the
core of this Dirac-vortex fibre, where the number of guiding modes equals the
winding number of the spatial vortex. The single-vortex design provides a
single-polarization single mode for a bandwidth as large as one octave.
