  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.
