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)].
Using a conventional Hall-bar geometry with a micro-metal strip on top of the surface, we demonstrate an electrical coherent control of nuclear spins in an AlGaAs/GaAs semiconductor heterostructure. A breakdown of integer quantum Hall (QH) effect is
utilized to dynamically polarize nuclear spins. By applying a pulse rf magnetic field with the metal strip, the quantum state of the nuclear spins shows Rabi oscillations, which is detected by measuring longitudinal voltage of the QH conductor.
