Dimensionality-dependent self-energy corrections and exchange-correlation potential in semiconductor nanostructures

Area of Science:

• Condensed Matter Physics
• Materials Science
• Quantum Mechanics

Background:

• The quasiparticle gap is crucial for semiconductor properties.
• Local Density Approximation (LDA) often underestimates this gap in nanostructures.
• Understanding dimensionality effects is key for designing novel electronic materials.

Purpose of the Study:

• To investigate the quasiparticle gap in semiconductor nanostructures across different dimensionalities.
• To compare theoretical predictions with values from the local density approximation.
• To identify the dominant factors contributing to the gap correction.

Main Methods:

• Development of general arguments using the GW (Greeen's function and W, the screened Coulomb interaction) approach.
• Numerical substantiation via a tight-binding version of the GW theory.
• Analysis of the quasiparticle gap's dependence on nanostructure dimensionality.

Main Results:

• The quasiparticle gap correction is primarily driven by a macroscopic surface self-polarization term.
• This surface self-polarization exhibits nonmonotonic behavior as dimensionality changes.
• Significant deviations from local density approximation predictions were observed.

Conclusions:

• Surface effects play a dominant role in determining the quasiparticle gap of semiconductor nanostructures.
• The GW approach provides a more accurate description than LDA for these systems.
• The nonmonotonic dependence on dimensionality highlights the complexity of quantum confinement in nanostructures.