  We prove sharp pointwise decay estimates for critical Dirac equations on
$\mathbb{R}^n$ with $n\geq 2$. They appear for instance in the study of
critical Dirac equations on compact spin manifolds, describing blow-up
profiles, and as effective equations in honeycomb structures. For the latter
case, we find excited states with an explicit asymptotic behavior. Moreover, we
provide some classification results both for ground states and for excited
states.
