This paper presents the first experimental realization of a three-dimensional topological insulator, a material that exhibits topological surface states and bulk Dirac fermions. The study focuses on the compound Bi$_{0.9}$Sb$_{0.1}$, which is a semiconductor with strong spin-orbit coupling. The researchers used incident photon energy-modulated angle-resolved photoemission spectroscopy (IPEM-ARPES) to directly observe the bulk Dirac fermions and the topological surface states in this material. They found that the bulk of Bi$_{0.9}$Sb$_{0.1}$ exhibits a three-dimensional Dirac point, and the surface states are gapless and topologically protected. These surface states are analogous to the edge states in a quantum spin Hall insulator, but exist in three dimensions. The study also shows that the surface states are protected by time-reversal symmetry, and their topological nature is determined by the $Z_2$ invariant. The results suggest that Bi$_{0.9}$Sb$_{0.1}$ is a topological insulator with a negative $Z_2$ invariant, and its surface states are topologically non-trivial. The findings have implications for the development of next-generation quantum computing devices, as they suggest that the material could be used to create devices with topologically protected spin-textured edge-surface currents. The study also provides a comprehensive mapping of the topological Dirac insulator's gapless surface modes, and confirms the existence of a Kramers point at the sample's boundary. The results demonstrate the potential of Bi$_{0.9}$Sb$_{0.1}$ as a novel quantum material with unique electronic properties.This paper presents the first experimental realization of a three-dimensional topological insulator, a material that exhibits topological surface states and bulk Dirac fermions. The study focuses on the compound Bi$_{0.9}$Sb$_{0.1}$, which is a semiconductor with strong spin-orbit coupling. The researchers used incident photon energy-modulated angle-resolved photoemission spectroscopy (IPEM-ARPES) to directly observe the bulk Dirac fermions and the topological surface states in this material. They found that the bulk of Bi$_{0.9}$Sb$_{0.1}$ exhibits a three-dimensional Dirac point, and the surface states are gapless and topologically protected. These surface states are analogous to the edge states in a quantum spin Hall insulator, but exist in three dimensions. The study also shows that the surface states are protected by time-reversal symmetry, and their topological nature is determined by the $Z_2$ invariant. The results suggest that Bi$_{0.9}$Sb$_{0.1}$ is a topological insulator with a negative $Z_2$ invariant, and its surface states are topologically non-trivial. The findings have implications for the development of next-generation quantum computing devices, as they suggest that the material could be used to create devices with topologically protected spin-textured edge-surface currents. The study also provides a comprehensive mapping of the topological Dirac insulator's gapless surface modes, and confirms the existence of a Kramers point at the sample's boundary. The results demonstrate the potential of Bi$_{0.9}$Sb$_{0.1}$ as a novel quantum material with unique electronic properties.