  Experiments have observed superconductivity in atomically-thin metallic
layers deposited on semiconducting substrates. As in any superconductor, it is
important to determine the structure of the superconducting pairing function in
order to reveal the mechanism responsible for superconductivity. To that end,
we study the possible superconducting states of two-dimensional triangular
lattices. We calculate the quasiparticle interference (QPI) patterns which
would result from various nearest-neighbor pairing order parameters, and show
how the QPI can be used to distinguish between those order parameters. The QPI
patterns are the momentum-space representations of real-space local
density-of-states fluctuations: the QPI signal at momentum $q$ reveals the
strength of scattering processes at that momentum transfer. We show how
characteristic differences between scattering from charge disorder (i.e.
impurities) and from order-parameter disorder (i.e. vortices) can be used to
identify the angular momentum of the superconducting pairs.
