Enhancement and suppression of tunneling by controlling symmetries of a potential barrier

We present a class of two-dimensional (2D) systems which shows a counterintuitive property that contradicts a semiclassical intuition: A 2D quantum particle ``prefers'' tunneling through a barrier rather than traveling above it. Viewing the one-particle 2D system as a system of two 1D particles, it is demonstrated that this effect occurs due to a specific symmetry of the barrier that forces excitations of the interparticle degree of freedom that, in turn, lead to the appearance of an effective potential barrier even though there is no ``real'' barrier. This phenomenon cannot exist in 1D.