  Few-body correlations emerging in two-dimensional harmonically trapped
mixtures, are comprehensively investigated. The presence of the trap leads to
the formation of atom-dimer and trap states, in addition to trimers. The Tan's
contacts of these eigenstates are studied for varying interspecies scattering
lengths and mass ratio, while corresponding analytical insights are provided
within the adiabatic hyperspherical formalism. The two- and three-body
correlations of trimer states are substantially enhanced compared to the other
eigenstates. The two-body contact of the atom-dimer and trap states features an
upper bound regardless of the statistics, treated semi-classically and having
an analytical prediction in the limit of large scattering lengths. Such an
upper bound is absent in the three-body contact. Interestingly, by tuning the
interspecies scattering length the contacts oscillate as the atom-dimer and
trap states change character through the existent avoided-crossings in the
energy spectra. For thermal gases, a gradual suppression of the involved two-
and three-body correlations is evinced manifesting the impact of thermal
effects. Moreover, spatial configurations of the distinct eigenstates ranging
from localized structures to angular anisotropic patterns are captured. Our
results provide valuable insights into the inherent correlation mechanisms of
few-body mixtures which can be implemented in recent ultracold atom experiments
and will be especially useful for probing the crossover from few- to many-atom
systems.
