Tunable Kondo effect and spin textures on topological insulators surfaces*

We consider screening of a spin-$1 / 2$ impurity at the surface of a topological insulator, and show that the very existence of Kondo screening strongly depend on details of the bulk material and surface preparation whose details are encoded in time-reversal preserving boundary conditions for electronic wavefunctions. We investigate in detail the formation of the Kondo resonance by studying the "orbital-flip" processes that screen the impurity spin in the resulting strongly spin-orbit coupled system. This mechanism gives rise to spin textures that can be used to experimentally probe signatures of a Kondo resonance in topological insulators, and we give examples relevant to specific materials.