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The criteria for strong correlations on surfaces of three-dimensionaltopological insulators are discussed. Usually, the Coulomb repulsion at suchsurfaces is too weak for driving a phase transition to a strongly correlatedregime. I discuss a mechanism and possibilities of its experimentalimplementation by which the strength of the Coulomb interaction can be tunedover a wide range. In the strongly interacting regime, the surface states aregapped, even though the topological classification of the bulk band structurepredicts gapless surface states.

Strong correlations at topological insulator surfaces and the breakdown of the bulk-boundary correspondence