Facet formation in the negative quenched Kardar-Parisi-Zhang equation

The quenched Kardar-Parisi-Zhang equation with negative nonlinear term shows a first order pinningdepinning ~PD! transition as the driving force F is varied. We study the substrate-tilt dependence of the dynamic transition properties in 111 dimensions. At the PD transition, the pinned surfaces form a facet with a characteristic slope sc as long as the substrate tilt m is less than sc . When m,sc , the transition is discontinuous and the critical value of the driving force Fc(m) is independent of m, while the transition is continuous and Fc(m) increases with m when m.sc . We explain these features from a pinning mechanism involving a localized pinning center and the self-organized facet formation. @S1063-651X~99!12602-3#