Discussion Overview
The discussion revolves around the formation of the Fermi surface in a 2D tight binding model, specifically questioning how it can be a perfect square given the dispersion characteristics. Participants also explore concepts related to electron occupancy in lattice sites and the implications for the chemical potential.
Discussion Character
- Exploratory
- Technical explanation
- Conceptual clarification
- Debate/contested
Main Points Raised
- One participant questions how the Fermi surface can be a perfect square when the dispersion does not appear to support this conclusion.
- Another participant suggests that both tight binding and perturbation theory can explain the formation of a square Fermi surface.
- There is a clarification that the half-filled case corresponds to one electron per lattice site, while two electrons would indicate a completely filled case.
- A later reply raises the issue of calculating the Fermi level for practical applications, particularly in density functional theory (DFT) software, and questions the effectiveness of such calculations.
Areas of Agreement / Disagreement
Participants express differing views on the relationship between the dispersion and the shape of the Fermi surface, indicating that the discussion remains unresolved with multiple competing perspectives on the topic.
Contextual Notes
Participants have not fully resolved the assumptions regarding the dispersion characteristics and their implications for the Fermi surface shape. There are also unresolved questions about the electron occupancy and its relation to the chemical potential.
