Epitaxial growth and erosion on (001) crystal surfaces: Far-from-equilibrium transitions, intermediary states, and vertical asymmetry

General phenomenology of multilayer epitaxial growth and erosion on square symmetry crystal surfaces is discussed within a unified model. We elucidate recently observed 45\ifmmode^\circ\else\textdegree\fi{} rotation transitions between pyramidal states on (001) surfaces. We predict and characterize novel intermediary states of many-sided pyramids ubiquitously intervening in these transitions and causing an enhanced roughening. We elucidate the actual effects of the elusive vertical (pyramid-pit) growth asymmetry on the multitude of states on (001) crystal surfaces.