Shell model extension to the valence force field: application to single-layer black phosphorus

Area of Science:

• Condensed Matter Physics
• Materials Science
• Computational Chemistry

Background:

• Traditional valence force field models often neglect electronic polarization.
• Accurate inter-atomic potentials are crucial for understanding material properties like phonon behavior.
• Single-layer black phosphorus exhibits unique electronic and vibrational characteristics.

Purpose of the Study:

• To extend the valence force field model by incorporating electronic polarization.
• To parameterize this enhanced model for single-layer black phosphorus using density functional theory.
• To investigate the impact of induced dipole interactions on phonon modes, particularly near the Brillouin zone center.

Main Methods:

• Parameterization of an extended valence force field model.
• Utilizing density functional theory (DFT) calculations as a reference.
• Fitting the phonon dispersion relation across the entire Brillouin zone.
• Analyzing the effect of induced dipole interactions on long-wavelength modes.

Main Results:

• The enhanced model successfully reproduces the phonon dispersion relation for single-layer black phosphorus.
• Inclusion of induced dipole interactions significantly damps the frequencies of near-Γ point infrared-active modes.
• The model's predictions show strong agreement with experimental observations.
• The parameterization method is adaptable to other materials, especially two-dimensional crystals.

Conclusions:

• The proposed extended valence force field model accurately captures the influence of electronic polarization on inter-atomic potentials.
• This approach provides a more refined description of vibrational properties in materials like black phosphorus.
• The methodology offers a versatile tool for studying phonon behavior in various two-dimensional materials.