  We analyze and observe the Fock-Darwin (FD) states in a circular n-p junction
(CNPJ) of topological surface states. Theoretically, in the CNPJ induced by the
sub-surface point charge, the FD states of Dirac fermions are found to have a
unique core-shell structure of trapped electrons and holes. The interplay
between them is highly tunable by the magnetic field, which has no analog in
their conventional counterparts and even in FD states of Dirac fermions
confined by the most-studied parabolic-like potentials. A modified
Einstein-Brillouin-Keller method is introduced to derive the electron-core
states semiclassically. Experimentally, we obtain the clearly resolved FD
states of topological surface states up to 14 Tesla which are very different
from those of conventional electrons. Our data also visualizes directly
directly the field-dependent potential landscape that may be modified by the
electron-electron interactions in a CNPJ at the surface of a three-dimensional
topological insulator thin film. Our findings signal the high tunability of the
FD states of topological surface states in CNPJs that can be obtained by
molecular beam epitaxy.

Mesoscale and Nanoscale Physics;Materials Science