Phonon dispersion in two-dimensional solids from atomic probability distributions

Area of Science:

• Condensed Matter Physics
• Materials Science
• Computational Physics

Background:

• Phonon dispersion relations are crucial for understanding material properties.
• Calculating these relations accurately, especially at finite temperatures and for 2D materials, presents computational challenges.
• Existing methods may not fully capture anharmonic effects or are computationally intensive.

Purpose of the Study:

• To develop a novel harmonic linear response (HLR) method for calculating phonon dispersion relations.
• To enable accurate calculations from equilibrium simulations at finite temperatures.
• To investigate anharmonic effects in two-dimensional materials.

Main Methods:

• The harmonic linear response (HLR) method is proposed, utilizing equilibrium path integral simulations.
• The method analyzes the centroid density to determine linear response.
• In the classical limit, it relates to covariance matrix diagonalization of atomic fluctuations.

Main Results:

• The HLR method's validity was confirmed for graphene monolayer, bilayer, and graphane.
• Anharmonic effects were demonstrated in graphene's phonon dispersion relations.
• Temperature dependence of kinetic energy, E_2g mode frequency, and elastic moduli were calculated.

Conclusions:

• The HLR method provides an effective way to compute phonon dispersion relations for 2D materials.
• The study highlights the significance of anharmonic effects on graphene's properties.
• This method offers a pathway for more accurate material property predictions at finite temperatures.