Three-dimensional topological insulators are a new state of quantum matter with a bulk gap and odd number of relativistic Dirac fermions on the surface. By investigating the surface state of Bi2Te3 with angle-resolved photoemission spectroscopy, we demonstrate that the surface state consists of a single nondegenerate Dirac cone. Furthermore, with appropriate hole doping, the Fermi level can be tuned to intersect only the surface states, indicating a full energy gap for the bulk states. Our results establish that Bi2Te3 is a simple model system for the three-dimensional topological insulator with a single Dirac cone on the surface. The large bulk gap of Bi2Te3 also points to promising potential for high-temperature spintronics applications.

The remarkable properties of atomically-thin semiconducting TMD layers include an indirect-to-direct bandgap crossover 1, 2, 9 , field-induced transport with high on-off ratios 16 , 3 valley selective circular dichroism [3][4][5][6] , and strong photovoltaic response 17,18 . Fundamental understanding of the electron/hole quasiparticle band structure and many-body interactions in 2D TMDs, however, is still lacking. Enhanced Coulomb interactions due to low-dimensional effects are expected to increase the quasiparticle bandgap as well as to cause electron-hole pairs to form more strongly bound excitons [10][11][12][13] . Untangling such many-body effects in single-layer TMDs requires measurement of both the electronic bandgap and the optical bandgap, the most fundamental parameters for transport and optoelectronics, respectively. The electronic bandgap (E g ) characterizes single-particle (or quasiparticle) excitations and is defined by the sum of the energies needed to separately tunnel an electron and a hole into monolayer MoSe 2 . The optical bandgap (E opt ), on the other hand, describes the energy required to create an exciton, a correlated two-particle electron-hole pair, via optical absorption. The difference in these energies (E g -E opt ) directly yields the exciton binding energy (E b ) (Fig. 2a). Here we provide evidence for Coulomb driven quasiparticle bandgap renormalization and unusually strong exciton stability in 2D TMD through direct determination of both E g and E opt via STS and PL spectroscopy, respectively. STS and PL measurements were carried out on the same high-quality sub-monolayer MoSe 2 films grown on epitaxial bilayer graphene (BLG) on a 6H-SiC(0001) substrate.Because the MoSe 2 surface coverage for our sample was ~ 0.8 ML, we were able to simultaneously image the MoSe 2 monolayer and the underlying graphene substrate using scanning tunneling microscopy (STM). We experimentally investigated both the electronic structure and the optical transitions in monolayer MoSe 2 /BLG by combining STS and PL spectroscopy. Fig. 2b shows a typical STM dI/dV spectrum acquired on monolayer MoSe 2 /BLG. The observed electronic structure is dominated by a large electronic bandgap surrounded by features labeled V 1-4 in the valence band (VB) and C 1 in the conduction band (CB). The MoSe 2 band edges are best determined by taking the logarithm of dI/dV, as shown in Fig. 2d.There the VB maximum (VBM) for monolayer MoSe 2 is seen to be located at -1.55 ± 0.03 V and the CB minimum (CBM) at 0.63 ± 0.02 V. The relative position of E F (V bias = 0 V) with respect to the band edges reveals n-type doping for our samples, although with 5 a very low carrier concentration. We tentatively attribute the n-doping of our MoSe 2 samples to intrinsic point defects such as vacancies and/or lattice antisites, which have been found to be responsible for n-doping in similar materials 20 . Our STS measurements yield a value for the single-particle electronic bandgap of E g = E CBM -E VBM = 2.18 eV ± 0.04 eV. The uncertainty ...

Three-dimensional (3D) topological Dirac semimetals (TDSs) represent an unusual state of quantum matter that can be viewed as "3D graphene." In contrast to 2D Dirac fermions in graphene or on the surface of 3D topological insulators, TDSs possess 3D Dirac fermions in the bulk. By investigating the electronic structure of Na3Bi with angle-resolved photoemission spectroscopy, we detected 3D Dirac fermions with linear dispersions along all momentum directions. Furthermore, we demonstrated the robustness of 3D Dirac fermions in Na3Bi against in situ surface doping. Our results establish Na3Bi as a model system for 3D TDSs, which can serve as an ideal platform for the systematic study of quantum phase transitions between rich topological quantum states.

Three-dimensional (3D) topological Dirac semimetals (TDSs) are a recently proposed state of quantum matter that have attracted increasing attention in physics and materials science. A 3D TDS is not only a bulk analogue of graphene; it also exhibits non-trivial topology in its electronic structure that shares similarities with topological insulators. Moreover, a TDS can potentially be driven into other exotic phases (such as Weyl semimetals, axion insulators and topological superconductors), making it a unique parent compound for the study of these states and the phase transitions between them. Here, by performing angle-resolved photoemission spectroscopy, we directly observe a pair of 3D Dirac fermions in Cd3As2, proving that it is a model 3D TDS. Compared with other 3D TDSs, for example, β-cristobalite BiO2 (ref. 3) and Na3Bi (refs 4, 5), Cd3As2 is stable and has much higher Fermi velocities. Furthermore, by in situ doping we have been able to tune its Fermi energy, making it a flexible platform for exploring exotic physical phenomena.