  We investigate light beam propagation along the interface between linear and
nonlinear media with parity-time PT symmetry, and derive an equation governing
the beam propagation. A novel class of two-dimensional PT surface solitons are
found analytically and numerically, and checked to be stable over a wide range
of PT potential structures and parameters. These surface solitons do not
require a power threshold. The transverse power flow across beam is examined
within the solitons and found to be caused by the nontrivial phase structure of
the solitons. PT surface solitons are possibly observed experimentally in
photorefractive crystals.
