Theoretical study of the band structure for multilayer germanane under external strain

Applying external strain is an effective approach for tuning the bandgap in germanane. However, recent investigations have been primarily limited to the study of biaxial tensile strain for monolayer germanane, while a comprehensive study of multilayer germanane under various strain types has not been reported to date. To address this issue, band structures for monolayer and multilayer germanane under different strain types (including uniaxial and biaxial strain, compressive and tensile strain) are investigated using a first-principle method based on density functional theory combined with a GGA+U method and supercell models. The results indicate that the interplay between different layers does not significantly influence the shape of the band structure when applying external strain to multilayer germanane. For both monolayer and multilayer germanane, the variation in the bandgap under biaxial or uniaxial strain is highly different. The materials exhibit direct energy bands when under tensile strain, while they show indirect bandgap areas when under compressive strain. To uncover the physical origin underlying this behavior, the projected band, projected density of states, charge density distribution, changes in bond length and bond angle for six-layer germanane are analyzed. These results provide a comprehensive theoretical guidance for the strain energy band engineering of germanane, which may present new potential applications in the field of electronic devices and optoelectronic devices. (paper)