Timeline for How to show that the electrons responsible for a current have an energy within $k_BT$ of the Fermi energy?
Current License: CC BY-SA 4.0
23 events
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| Jun 3, 2019 at 15:03 | history | edited | Jeffrey J Weimer | CC BY-SA 4.0 |
tightened the description
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| May 30, 2019 at 17:37 | history | edited | Jeffrey J Weimer | CC BY-SA 4.0 |
added 443 characters in body
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| May 30, 2019 at 17:12 | comment | added | untreated_paramediensis_karnik | Let us continue this discussion in chat. | |
| May 30, 2019 at 16:46 | comment | added | Jeffrey J Weimer | Your fallacy is to believe that only those electrons promoted by the E field are free to carry current and indeed are the only electrons that carry current. I have re-written my answer to frame this fallacy for what it is. | |
| May 30, 2019 at 16:44 | history | edited | Jeffrey J Weimer | CC BY-SA 4.0 |
completely re-wrote description to use Fermi surface
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| May 30, 2019 at 16:12 | history | undeleted | Jeffrey J Weimer | ||
| May 30, 2019 at 16:11 | history | deleted | Jeffrey J Weimer | via Vote | |
| May 30, 2019 at 14:35 | comment | added | untreated_paramediensis_karnik | No, I do not believe only electrons at the surface can be perturbed by an E field. I have a window range that I calculated, and is proportional to the electric field's strength but does not contain $k_BT$ (though apparently it should!). | |
| May 30, 2019 at 14:29 | comment | added | Jeffrey J Weimer | So, is your confusion that you believe that only electrons EXACTLY at the surface of the sphere can be perturbed by the field? Do you not allow for a $k_BT$ perturbation already? | |
| May 30, 2019 at 14:28 | history | edited | Jeffrey J Weimer | CC BY-SA 4.0 |
removed statement about Fermi sphere
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| May 30, 2019 at 14:25 | comment | added | untreated_paramediensis_karnik | About the muffin-tin potential, it is an unnecessary over complication to the problem. There is no need to invoke the lattice potential at all, I could repeat the same arguments as I already wrote above. | |
| May 30, 2019 at 14:22 | comment | added | untreated_paramediensis_karnik | I have seen the link, and nowhere it is claimed that the electrons inside the sphere are bound (to the nuclei as you imply) electrons. They are all free electrons. The only place "bound" appears in the reference you give is to state that the energy of these free electrons is lesser than those right at the surface. Again, this has nothing to do with "bound to the nuclei electrons". | |
| May 30, 2019 at 14:21 | comment | added | Jeffrey J Weimer | The muffin-tin potential is as classic as it gets. It is not esoteric stuff. It is an analogy to learning about the motion of a car down an incline using Newton's laws or using conservation of energy. | |
| May 30, 2019 at 14:06 | comment | added | untreated_paramediensis_karnik | I see your point of view now. The thing is, the answer can come out within the free electron model. It's as if I had asked how to solve a simple classical mechanics problem and you offer an answer that deals with general relativity, dark matter and black holes. But you also made wrong statements. For example, with your latest edit regarding the states inside the Fermi sphere, you claim that they are bound electrons. This is wrong, these are free electrons, the bound electrons aren't displayed at all in that picture. | |
| May 30, 2019 at 13:47 | history | edited | Jeffrey J Weimer | CC BY-SA 4.0 |
added 527 characters in body
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| May 30, 2019 at 13:35 | comment | added | untreated_paramediensis_karnik | I feel did not post any insult to your content. Feel free to report my posts if you think so, and moderators will take over. The free electron model (en.wikipedia.org/wiki/Free_electron_model) is an idealized model of a metal that takes into account PEP. It works well for most alkali metals where the effects of the lattice potential is not very strong. It has its limitations, but it is used to understand how to compute the conductivities and other basic properties of metals. It is much better than Drude's original model (which is still taught). | |
| May 30, 2019 at 13:30 | history | edited | Jeffrey J Weimer | CC BY-SA 4.0 |
added 143 characters in body
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| May 30, 2019 at 13:18 | comment | added | untreated_paramediensis_karnik | taken into account. This is only from lowly doped semiconductors that the PEP starts to become less relevant. But in metals, it is of utmost importance to understand any basic property, like the electrical and thermal conductivities. | |
| May 30, 2019 at 13:14 | comment | added | untreated_paramediensis_karnik | Also I'm not sure why you complicate things by mentioning the bound electrons. My question would still stand if I replaced "metal" by "free electron gas". It would still be entirely valid, and your point regarding the lattice potential(s), useless... I just saw your edit that now says that free (unbound) electrons do not satisfy the Pauli exclusion principle. This is wrong. A free electron gas for example satisfies the PEP, and alkali metals are close to that ideal model. The density of electrons in metals is so high compared to an ordinary gas at atmosphere pressure that the PEP has to be | |
| May 30, 2019 at 13:13 | history | edited | Jeffrey J Weimer | CC BY-SA 4.0 |
added 416 characters in body
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| May 30, 2019 at 13:07 | comment | added | untreated_paramediensis_karnik | Essentially your answer is that the premise of my question is wrong. Then I would like to know where Datta (and many, many others) went wrong. | |
| May 30, 2019 at 13:05 | comment | added | untreated_paramediensis_karnik | "ALL free electrons can move, regardless of their energy above the Fermi energy" Do you mean interact instead of move? Or "change their energy"? Because of course, all but 2 electrons are constantly moving if we consider a Fermi gas. (yes, there are 2 electrons with exactly zero energy, though they are still spread across the whole sample). | |
| May 30, 2019 at 13:02 | history | answered | Jeffrey J Weimer | CC BY-SA 4.0 |