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After the theoretical prediction that SmB$_6$ is a topological Kondo insulator, there has been an explosion of studies on the SmB$_6$ surface. However, there is not yet an agreement on even the most basic quantities such as the surface carrier density and mobility. In this paper, we carefully revisit Corbino disk magnetotransport studies to find those surface transport parameters. We first show that subsurface cracks exist in the SmB$_6$ crystals, arising both from surface preparation and during the crystal growth. We provide evidence that these hidden subsurface cracks are additional conduction channels, and the large disagreement between earlier surface SmB$_6$ studies may originate from previous interpretations not taking this extra conduction path into account. We provide an update of a more reliable magnetotransport data than the previous one (Phys. Rev. B 92, 115110) and find that the orders-of-magnitude large disagreements in carrier density and mobility come from the surface preparation and the transport geometry rather than the intrinsic sample quality. From this magnetotransport study, we find an updated estimate of the carrier density and mobility of 2.71$\times$10$^{13}$ (1/cm$^2$) and 104.5 (cm$^{2}$/V$\cdot$sec), respectively. We compare our results with other studies of the SmB$_6$ surface. By this comparison, we provide insight into the disagreements and agreements of the previously reported angle-resolved photoemission spectroscopy, scanning tunneling microscopy, and magnetotorque quantum oscillations measurements.

We performed angle resolved photoemission (ARPES) experiments on Bi2Te3 with circularly polarized light. ARPES data show very strong circular dichroism, indicating existence of orbital angular momentum (OAM). Moreover, the alignment of OAM is found to have a strong binding energy dependence. Such energy dependence comes from a relatively strong band warping effect in Bi2Te3 compared to Bi2Se3. OAM close to Dirac point has an ideal chiral structure (sin ?) without out-of-plane component. Warping effect comes in as the binding energy decreases and circular dichroism along a constant energy contour can no longer be explained by a simple sin? function but requires a sin3? term. When the warping effect becomes even stronger near the Fermi energy, circular dichroism gains an additional sin6? term. Such behavior is found to be compatible with the theoretically predicted OAM structure.

We performed angle-resolved photoemission (ARPES) experiments on Bi2Te3 with circularly polarized light. ARPES data show very strong circular dichroism, indicating the existence of orbital angular momentum (OAM). Moreover, the alignment of OAM is found to have a strong binding energy dependence. Such energy dependence comes from a relatively strong band warping effect in Bi2Te3 compared to Bi2Se3. OAM close to the Dirac point has an ideal chiral structure (sinθ) without an out-of-plane component. The warping effect comes in as the binding energy decreases, and circular dichroism along a constant energy contour can no longer be explained by a simple sinθ function but requires a sin3θ term. When the warping effect becomes even stronger near the Fermi energy, circular dichroism gains an additional sin6θ term. Such behavior is found to be compatible with the theoretically predicted OAM structure.