Selective trapping of hexagonally warped topological surface states in a triangular quantum corral

The surface of a three-dimensional topological insulator (TI) hosts two-dimensional massless Dirac fermions (DFs), the gapless and spin-helical nature of which leads to their high transmission through surface defects or potential barriers. Here, we report the behaviors of topological surface states (TSS) in a triangular quantum corral (TQC) which, unlike a circular corral, is supposed to be totally transparent for DFs. By real-space mapping of the electronic structure of TQCs, both the trapping and detrapping behaviors of the TSS are observed. The selection rules are found to be governed by the geometry and spin texture of the constant energy contour of TSS upon the strong hexagonal warping in Bi₂Te₃. Our work indicates the extended nature of TSS and elucidates the selection rules of the trapping of TSS in the presence of a complicated surface state structure, giving insights into the effective engineering of DFs in TIs.