  We study the ground-state physics of a single-component Haldane model on a
hexagonal two-leg ladder geometry with a particular focus on strongly
interacting bosonic particles. We concentrate our analysis on the regime of
less than one particle per unit-cell. As a main result, we observe several
Meissner-like and vortex-fluid phases both for a superfluid as well as a
Mott-insulating background. Furthermore, we show that for strongly interacting
bosonic particles an unconventional vortex-lattice phase emerges, which is
stable even in the regime of hardcore bosons. We discuss the mechanism for its
stabilization for finite interactions by a means of an analytical
approximation. We show how the different phases may be discerned by measuring
the nearest- and next-nearest-neighbor chiral currents as well as their
characteristic momentum distributions.
