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Definitive Surface Magnetotransport Study of SmB$_{6}$

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.