Symmetry Breaking with a Slant: Topological Defects after an Inhomogeneous Quench

We show that, in second-order phase transformations induced by an inhomogeneous quench, the density of topological defects is drastically suppressed as the velocity with which the quench propagates becomes smaller than the speed at which the front of the broken symmetry phase spreads. The velocity of the broken symmetry phase front is approximately given by the ratio of the healing length to relaxation time at freeze-out, that is at the instant when the critical slowing down results in a transition from the adiabatic to the impulse behavior in the order parameter. Experimental implications are briefly discussed.