Using first-principles calculations we show that face-centered cubic Dy(111) ultrathin films exhibit height selective stability. The origin of such height selection can be attributed to the interplay between the localized surface states and surface resonance states due to electron confinement effects. Such effect could be utilized to manipulate the film thickness at the atomic level to achieve desirable film properties or to control the growth of nanostructures on the thin film for various applications.
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