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 components 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.
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