Discussion Overview
The discussion revolves around the calculation of the Chern number in a specific system, exploring whether it can yield non-integer values and the implications of such results. Participants examine the theoretical foundations and practical methods for calculating the Chern number, including the use of tight-binding Hamiltonians and numerical approaches.
Discussion Character
- Exploratory, Technical explanation, Debate/contested, Homework-related
Main Points Raised
- One participant reports obtaining a Chern number of 0.9 and questions whether this indicates an error or if it can be considered as 1.
- Another participant asserts that the Chern number should generally be an integer but acknowledges that non-integer values may arise in metallic systems due to the lack of a gapped band structure at the Fermi level.
- There is mention of workarounds to define an integer Chern number despite non-integer calculations in certain contexts.
- A participant inquires about the specific methods used for calculation, suggesting that numerical adjustments might be necessary for better results.
- Further discussion includes the use of a tight-binding Hamiltonian and Kubo formula in MATLAB for the calculations, with questions about the validity of obtaining values like 1.93 or 0.7.
- One participant requests assistance with MATLAB code, indicating a willingness to share their code for review in case of errors.
Areas of Agreement / Disagreement
Participants express differing views on the nature of the Chern number, with some asserting it should be an integer while others recognize the possibility of non-integer values in specific systems. The discussion remains unresolved regarding the implications of these non-integer results and the methods for calculation.
Contextual Notes
Participants mention the dependence on the specific system being analyzed and the potential limitations of numerical methods in calculating the Chern number. There is also a reference to a specific paper that may provide further context for the calculations being discussed.