Massless Dirac electrons in condensed matter have attracted considerable attention. Unlike conventional electrons, Dirac electrons are described in the form of two-component wave functions. In the surface state of topological insulators, these two co
mponents are associated with the spin degrees of freedom, hence governing the magnetic properties. Therefore, the observation of the two-component wave function provides a useful clue for exploring the novel spin phenomena. Here we show that the two-component nature is manifested in the Landau levels (LLs) whose degeneracy is lifted by a Coulomb potential. Using spectroscopic-imaging scanning tunneling microscopy, we visualize energy and spatial structures of LLs in a topological insulator Bi2Se3. The observed potential-induced LL splitting and internal structures of Landau orbits are distinct from those in a conventional electron system and are well reproduced by a two-component model Dirac Hamiltonian. Our model further predicts non-trivial energy-dependent spin-magnetization textures in a potential variation. This provides a way to manipulate spins in the topological surface state.
We investigate Dirac fermions on the surface of the topological insulator Bi2Se3 using scanning tunneling spectroscopy. Landau levels (LLs) are observed in the tunneling spectra in a magnetic field. In contrast to LLs of conventional electrons, a fie
ld independent LL appears at the Dirac point, which is a hallmark of Dirac fermions. A scaling analysis of LLs based on the Bohr-Sommerfeld quantization condition allowed us to determine the dispersion of the surface band. Near the Fermi energy, fine peaks mixed with LLs appear in the spectra, which may be responsible for the anomalous magneto-fingerprint effect [J. G. Checkelsky et al., Phys. Rev. Lett. 103, 246601 (2009)].
High-transition-temperature (high-Tc) superconductivity is ubiquitous in the cuprates containing CuO2 planes but each cuprate has its own character. The study of the material dependence of the d-wave superconducting gap (SG) should provide important
insights into the mechanism of high-Tc. However, because of the pseudogap phenomenon, it is often unclear whether the energy gaps observed by spectroscopic techniques really represent the SG. Here, we report spectroscopic imaging scanning tunneling microscopy (SI-STM) studies of nearly-optimally-doped Ca2-xNaxCuO2Cl2 (Na-CCOC) with Tc = 25 ~ 28 K. They enable us to observe the quasi-particle interference (QPI) effect in this material, through which unambiguous new information on the SG is obtained. The analysis of QPI in Na-CCOC reveals that the SG dispersion near the gap node is almost identical to that of Bi2Sr2CaCu2Oy (Bi2212) at the same doping level, while Tc of Bi2212 is 3 times higher than that of Na-CCOC. We also find that SG in Na-CCOC is confined in narrower energy and momentum ranges than Bi2212. This explains at least in part the remarkable material dependence of Tc
