Interfaces with a single growth inhomogeneity and anchored boundaries

Area of Science:

• Condensed matter physics
• Statistical mechanics
• Surface growth phenomena

Background:

• Understanding surface dynamics is crucial in materials science and nanotechnology.
• One-dimensional growth models provide simplified yet insightful frameworks for studying complex interfacial phenomena.
• Localized inhomogeneities and boundary conditions significantly impact system evolution.

Purpose of the Study:

• To investigate the dynamics of a one-dimensional growth model with localized inhomogeneity and anchored boundaries.
• To analytically calculate roughening exponents in the stationary regime.
• To explore the relationship between the model's spectrum gap and its dynamic scaling behavior, particularly concerning morphological transitions and faceting.

Main Methods:

• Analytical calculation of roughening exponents using equilibrium stationary states.
• Mapping the stochastic evolution to a spin Hamiltonian.
• Numerical simulations to study scaling regimes and morphological transitions for vanishing spectrum gaps.
• Investigating faceting dynamics in gapful situations.

Main Results:

• Anchored boundary conditions drive the system towards an equilibrium stationary regime at large times.
• The spectrum gap of the related spin Hamiltonian directly relates to the dynamic scaling exponent.
• Vanishing spectrum gaps lead to slow morphological transitions and changes in scaling regimes.
• Non-vanishing (gapful) spectrum gaps result in the emergence of faceting dynamics.

Conclusions:

• The interplay between localized inhomogeneity and anchored boundaries dictates the long-time behavior of the 1D growth model.
• The spectrum gap serves as a critical parameter determining whether the system undergoes morphological transitions or exhibits faceting.
• This work provides a theoretical and numerical framework for understanding diverse scaling behaviors in driven interface systems.