  We show that two-dimensional Artin groups satisfy a strengthening of the Tits
alternative: their subgroups either contain a non-abelian free group or are
virtually free abelian of rank at most $2$.
  When in addition the associated Coxeter group is hyperbolic, we answer in the
affirmative a question of Wise on the subgroups generated by large powers of
two elements: given any two elements $a, b$ of a two-dimensional Artin group of
hyperbolic type, there exists an integer $n\geq 1$ such that $a^n$ and $b^n$
either commute or generate a non-abelian free subgroup.
