Prof.Dr . Stephanie Curnoe2026-06-142026-06-14https://dspace.academy.edu.ly/handle/123456789/2298In quantum mechanics, the state of a system is described by linear combinations of orthonormal vectors forming a basis set, and this orthonormal basis spans the Hilbert space, which is a linear vector space. It is topological when the Hilbert space has a nontrivial topology. Then, we can find different kinds of topological insulators depending on the topology of the Hilbert space. The non-trivial topology is a feature of gapped energy states, and as long as the energy gap remains open, the topology cannot change. However, because of the potential that confines electrons within the sample, there will be gapless states at the boundary.Topological insulators are materials that exhibit a qualitatively new aspect of quantum mechanics. Topological insulators are insulators in bulk but have gapless surface states which conduct. These gapless states must exist due to the topology of the band structure. Several dozens of such materials have been discovered, but most of them are weakly correlated band insulators. Samarium hexaboride a strong correlated Kondo insulator was proposed to be a 3D topological insulator in 2011 [6]. In this work, we examined whether samarium hexaboride is a topological insulator, or not by reviewing and reanalyzing all published experimental results to date.Topological Insulator