Timeline for Position space representation of tight-binding model with composite lattice
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
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| Jul 14, 2023 at 8:28 | answer | added | Karim Chahine | timeline score: 0 | |
| Jul 8, 2023 at 15:43 | comment | added | Frank Wang | What I mean by "having different dimensions on two sides" is that since in Fourier transforms, $k$ and $r$ transform into each other. So if now I add an additional index $\alpha$ it should add an additional degree of freedom. This statement is obviously flawed but I can't see why. | |
| Jul 8, 2023 at 15:36 | comment | added | Karim Chahine | What do you mean by "$\langle r| k_1, \alpha\rangle$ has different dimensions on two sides"? And also what does it mean that "$k$ is supposed to transform into $r$"?. The point is that the $r$ index should cover all lattice sites, this means you either interpret $r$ as a lattice site and so there are $NN_\alpha$ of those (with $N$ the number of unit cells and $N_\alpha$ the number of sites in a unit cell) or you give it the structure $(R,\alpha)$ with $R$ spanning just the unit cells and $\alpha$ being the internal degree of freedom. Whatever you choose, be consistent and it will make sense. | |
| Jul 8, 2023 at 15:21 | history | edited | Frank Wang | CC BY-SA 4.0 |
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| Jul 8, 2023 at 15:00 | history | asked | Frank Wang | CC BY-SA 4.0 |