Quantum interaction of steps and crystallization waves in 4He

Steps control crystal growth as well as the equilibrium shape of a facet and vicinal faces. In 4He at low temperatures, a step in a singular crystal plane is viewed as a moving elastic string. When a step oscillates, the superfluid flow transports material from a melting part to a growing part. If there are many parallel steps with a separation d, the oscillation spectrum is modified by the interference of the flow. As a result, the zero-point energy of the step increases, which leads to a d-2 repulsive interaction between steps. The oscillation spectrum of a stepped surface is calculated for the entire range of wave numbers. For k much-gt 1/d the steps oscillate individually, and for k much-lt 1/d they oscillate collectively as an anisotropic crystallization wave