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The surface of a three-dimensional topological insulator (TI) hosts two-dimensional massless Dirac fermions (DFs), the gapless and spin-helical nature of which yields many exotic phenomena, such as the immunity of topological surface states (TSS) to back-scattering. This leads to their high transmission through surface defects or potential barriers. Quantum corrals, previously elaborated on metal surfaces, can act as nanometer-sized electronic resonators to trap Schr\"odinger electrons by quantum confinement. It is thus intriguing, concerning their peculiar nature, to put the Dirac electrons of TSS to the test in similar circumstances. Here, we report the behaviors of TSS in a triangular quantum corral (TQC) fabricated by epitaxially growing Bi bilayer nanostructures on the surfaces of Bi2Te3 films. Unlike a circular corral, the TQC is supposed to be totally transparent for DFs. By mapping the electronic structure of TSS inside TQCs through a low-temperature scanning tunneling microscope in the real space, both the trapping and de-trapping behaviors of the TSS electrons 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. Careful analysis of the quantum interference patterns of quasi-bound states yields the corresponding wave vectors of trapped TSS, through which two trapping mechanisms favoring momenta in different directions are uncovered. 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., Comment: 31pages, 12figures(including supplementary materials)

The effects of spin-orbit coupling and symmetry breaking at the interface between a ferromagnet and heavy metal are particularly important for spin-based information storage and computation. Recent discoveries suggest they can create chiral spin structures (e.g. skyrmions), which have often been identified through the appearance of the bump/dip features of Hall signals, the so-called topological Hall effect (THE). In this work, however, we have present an unusual anomalous Hall effect (UAHE) in MnxGa/Pt bilayers and demonstrated that the features extremely similar to THE can be generated without involving any chiral spin structures. The low temperature magnetic force microscopy has been used to explore the magnetic field-dependent behavior of spin structures, and the UAHE as a function of magnetic field does not peak near the maximal density of magnetic bubbles. The results unambiguously evidence that the UAHE in MnxGa/Pt bilayers shows no correlation with chiral spin structures but is driven by the modified interfacial properties. The bump/dip features of Hall signals cannot be taken as an unambiguous signature for the emergence of chiral spin structures, and a wealth of underlying and interesting physics need explored.