We investigate light-beam propagation along the interface between linear and nonlinear media with parity-time symmetry. A novel class of two-dimensional localized surface modes (LSMs) is found analytically and numerically. If the potential is parity-time invariant along the direction parallel to the interface between the two media, stable LSMs can exist. Otherwise, if the potential is parity-time invariant along the direction perpendicular to the interface between the two media, there are no stable LSMs.
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