  The criteria for strong correlations on surfaces of three-dimensional
topological insulators are discussed. Usually, the Coulomb repulsion at such
surfaces is too weak for driving a phase transition to a strongly correlated
regime. I discuss a mechanism and possibilities of its experimental
implementation by which the strength of the Coulomb interaction can be tuned
over a wide range. In the strongly interacting regime, the surface states are
gapped, even though the topological classification of the bulk band structure
predicts gapless surface states.
