  Emergent lattices at mesoscopic length scales have evoked interest in several
recent contexts, e.g., in crystalline arrangements of skyrmions. It is a
challenging task to determine their collective excitations as the unit cells
are large and can contain complex textures. We address this issue in the oldest
known example of an emergent mesoscopic lattice, the vortex lattice in a
superfluid. We show that a tight binding approach can successfully describe
collective modes. We begin with a single isolated vortex in a two dimensional
system. With suitable pinning mechanims, the low energy excitations take the
form of localized pairing fluctuations. They can be viewed as wave-like
disturbances that propagate around the vortex centre, in the azimuthal
direction. In particular, the lowest energy excitations are gyrotropic and
breathing modes. The former corresponds to circular motion of the eye of the
vortex, while the latter represents an oscillation between sharper and broader
vortex profiles. These modes are `bosonic' analogues of atomic orbitals with
the vortex profile playing the role of the nuclear potential. Moving to a
sparse vortex lattice with well separated vortices, the single-vortex
excitations provide a convenient basis for finding normal modes. We derive an
analogue of Bloch's theorem in this context, revealing a non-trivial phase
contribution arising from the orbital field. We set up a tight binding
prescription and use it to explicitly determine the band structure of
excitations about a square vortex lattice. Our results can be tested in
ultracold atomic gases with synthetic magnetic fields.
