  Two-dimensional (2D) mobile carriers are a wellspring of quantum phenomena.
Among various 2D-carrier systems, such as field effect transistors and
heterostructures, polar materials hold a unique potential; the spontaneous
electric polarization in the bulk could generate positive and negative 2D
carriers at the surface. Although several experiments have shown ambipolar
carriers at the surface of a polar semiconductor BiTeI, their origin is yet to
be specified. Here we provide compelling experimental evidences that the
ambipolar 2D carriers at the surface of BiTeI are induced by the spontaneous
electric polarization. By imaging electron standing waves with spectroscopic
imaging scanning tunneling microscopy, we find that positive or negative
carriers with Rashba-type spin splitting emerge at the surface correspondingly
to the polar directions in the bulk. The electron densities at the surface are
constant independently of those in the bulk, corroborating that the 2D carriers
are induced by the spontaneous electric polarization. We also successfully
image that lateral $p$-$n$ junctions are formed along the boundaries of
submicron-scale domains with opposite polar directions. Our study presents a
novel means to endow non-volatile, spin-polarized, and ambipolar 2D carriers as
well as, without elaborate fabrication, lateral $p$-$n$ junctions of those
carriers at atomically-sharp interfaces.
