Peculiar Rashba spin texture induced by \({C}_{3v}\) symmetry on the Bi(111) surface revisited

When electrons are subject to a large external magnetic field, the conventional charge quantum Hall effect \cite{Klitzing,Tsui} dictates that an electronic excitation gap is generated in the sample bulk, but metallic conduction is permitted at the boundary. Recent theoretical models suggest that certain bulk insulators with large spin-orbit interactions may also naturally support conducting topological boundary states in the extreme quantum limit, which opens up the possibility for studying unusual quantum Hall-like phenomena in zero external magnetic field. Bulk Bi\(_{1-x}\)Sb\(_x\) single crystals are expected to be prime candidates for one such unusual Hall phase of matter known as the topological insulator. The hallmark of a topological insulator is the existence of metallic surface states that are higher dimensional analogues of the edge states that characterize a spin Hall insulator. In addition to its interesting boundary states, the bulk of Bi\(_{1-x}\)Sb\(_x\) is predicted to exhibit three-dimensional Dirac particles, another topic of heightened current interest. Here, using incident-photon-energy-modulated (IPEM-ARPES), we report the first direct observation of massive Dirac particles in the bulk of Bi\(_{0.9}\)Sb\(_{0.1}\), locate the Kramers' points at the sample's boundary and provide a comprehensive mapping of the topological Dirac insulator's gapless surface modes. These findings taken together suggest that the observed surface state on the boundary of the bulk insulator is a realization of the much sought exotic "topological metal". They also suggest that this material has potential application in developing next-generation quantum computing devices.

Recent theories and experiments have suggested that strong spin-orbit coupling effects in certain band insulators can give rise to a new phase of quantum matter, the so-called topological insulator, which can show macroscopic entanglement effects. Such systems feature two-dimensional surface states whose electrodynamic properties are described not by the conventional Maxwell equations but rather by an attached axion field, originally proposed to describe strongly interacting particles. It has been proposed that a topological insulator with a single spin-textured Dirac cone interfaced with a superconductor can form the most elementary unit for performing fault-tolerant quantum computation. Here we present an angle-resolved photoemission spectroscopy study and first-principle theoretical calculation-predictions that reveal the first observation of such a topological state of matter featuring a single-surface-Dirac-cone realized in the naturally occurring Bi\(_2\)Se\(_3\) class of materials. Our results, supported by our theoretical predictions and calculations, demonstrate that undoped compound of this class of materials can serve as the parent matrix compound for the long-sought topological device where in-plane surface carrier transport would have a purely quantum topological origin. Our study further suggests that the undoped compound reached via n-to-p doping should show topological transport phenomena even at room temperature.