Excitonic effects in solids described by time-dependent density-functional theory.

Area of Science:

• Condensed matter physics
• Quantum mechanics
• Materials science

Background:

• Excitonic effects significantly influence the optical properties of materials.
• Accurately capturing these effects within theoretical frameworks remains a challenge.

Purpose of the Study:

• To derive a novel exchange-correlation kernel within time-dependent density functional theory (TDDFT) that explicitly includes excitonic effects.
• To validate the efficacy of this kernel by comparing theoretical predictions with experimental data for bulk silicon.

Main Methods:

• Derivation of a static, nonlocal exchange-correlation kernel from the many-body Bethe-Salpeter equation.
• Incorporation of self-energy corrections and electron-hole interactions into the kernel.
• Application of the derived kernel to TDDFT calculations for bulk silicon.

Main Results:

• The derived exchange-correlation kernel successfully reproduces excitonic effects in bulk materials.
• The kernel accounts for both self-energy and electron-hole interaction, featuring a long-range Coulomb tail.
• The -alpha/q(2) divergency in the kernel was found crucial for continuum excitons, leading to excellent agreement with experimental absorption spectra for silicon.

Conclusions:

• The developed exchange-correlation kernel provides an accurate and efficient method for studying excitonic effects in condensed matter.
• This approach enhances the predictive power of TDDFT for optical properties of materials.
• The findings highlight the importance of specific kernel features, like the Coulomb tail, for capturing essential physical phenomena.