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The peculiar metallic electronic states observed in the Kondo insulator, samarium hexaboride (SmB$_6$), has stimulated considerable attention among those studying non-trivial electronic phenomena. However, experimental studies of these states have led to controversial conclusions mainly to the difficulty and inhomogeneity of the SmB$_6$ crystal surface. Here, we show the detailed electronic structure of SmB$_6$ with angle-resolved photoelectron spectroscopy measurements of the three-fold (111) surface where only two inequivalent time-reversal-invariant momenta (TRIM) exist. We observe the metallic two-dimensional state was dispersed across the bulk Kondo gap. Its helical in-plane spin polarisation around the surface TRIM suggests that SmB$_6$ is topologically non-trivial, according to the topological classification theory for weakly correlated systems. Based on these results, we propose a simple picture of the controversial topological classification of SmB$_6$.
Recent theoretical and experimental studies suggest that SmB$_6$ is the first topological Kondo insulator: A material in which the interaction between localized and itinerant electrons renders the bulk insulating at low temperature, while topological
The recent conjecture of a topologically-protected surface state in SmB$_6$ and the verification of robust surface conduction below 4 K have prompted a large effort to understand the surface states. Conventional Hall transport measurements allow curr
Strongly correlated electron systems show many exotic properties such as unconventional superconductity, quantum criticality, and Kondo insulating behavior. In addition, the Kondo insulator SmB6 has been predicted theoretically to be a 3D topological
The research effort prompted by the prediction that SmB$_6$ could be the first topological Kondo insulator has produced a wealth of new results, though not all of these seem compatible. A major discrepancy exists between scanning tunneling microscopy
We performed angle-resolved photoelectron spectroscopy of the Bi(111) surface to demonstrate that this surface support edge states of non-trivial topology. Along the $bar{Gamma}bar{M}$-direction of the surface Brillouin zone, a surface-state band dis