Why do we need to know "two-bands" Hall coefficient and magn

In summary, the conversation discusses the issue of a post not showing properly and the possible reasons for it. The topic of partially filled bands and Ohm's law is also brought up, with the formulas for Hall coefficient and magnetoresistance being mentioned. The conversation concludes with the issue being resolved in Safari but still appearing differently in Chrome.
  • #1
Philethan
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(Oh my god, why can't my post show normally? Some sentences just disappear, but I can still see them while editing. It's very weird. Can someone help me? I've reported.)I know only partially filled bands result in current density, and I think there must be not only 2 partially filled bands, but "several" partially filled bands. For each partially filled band, its Ohm's law is $$\mathbf{E}=\tilde{\rho}_{\text{n}}\:\mathbf{j}_{\text{n}},$$where the ##\tilde{\rho}_{\text{n}}## has the form:$$\tilde{\rho}_n=\begin{pmatrix}\rho_{\text{n}}&-R_{\text{n}}H\\R_{\text{n}}H&\rho_{\text{n}}\end{pmatrix}$$Furthermore, the total induced current is given by##\mathbf{E}=\tilde{\rho}\cdot\mathbf{j}##,with$$\tilde{\rho}=\left(\sum\tilde{\rho}_{\text{n}}^{-1}\right)^{-1}$$In Ashcroft & Mermin Solid State Physics textbook, it's said the Hall coefficient and magnetoresistance by only two bands are:$$R=\frac{R_1\rho_2^2+R_2\rho_1^2+R_1R_2(R_1+R_2)H^2}{(\rho_1+\rho_2)^2+(R_1+R_2)^2H^2}$$$$\rho=\frac{\rho_1\rho_2(\rho_1+\rho_2)+(\rho_1R_2^2+\rho_2R_1^2)H^2}{(\rho_1+\rho_2)^2+(R_1+R_2)^2H^2}$$Why do we need these two formulas if it's almost impossible to have only two partially filled bands? Thank you very much!
 
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berkeman said:
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Thanks so much. I found it doesn't show normally in Safari, but it's good in Chrome. Please help me check if there's something wrong with backend settings. Thank you so much :D Here's my screenshots.

It's Safari:
DDH7mLf.png
And it's Chrome:
KKxnSuz.png


Thank you so much!------------[Update]------------It works in Safari now. It's weird... Anyway, thanks :)

UVOdpzy.png
 

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1. Why is the Hall coefficient important in scientific research?

The Hall coefficient is an important parameter in the study of electronic and magnetic properties of materials. It provides information about the density and mobility of charge carriers, which are crucial for understanding the electrical conductivity and magnetic behavior of a material.

2. How does the Hall coefficient help in the characterization of materials?

The Hall coefficient can be used to determine the type of charge carriers (electrons or holes) in a material, as well as their concentration and mobility. This information is essential for identifying the electronic and magnetic properties of a material and can aid in material design and optimization for specific applications.

3. Why is it necessary to measure the Hall coefficient at different temperatures?

The Hall coefficient is temperature-dependent and can provide insight into the thermal properties of a material. By measuring the Hall coefficient at different temperatures, researchers can understand how charge carrier concentration and mobility change with temperature, which can further inform the material's electronic and magnetic behavior.

4. How does the Hall effect play a role in the two-band Hall coefficient and magnetoresistance?

The Hall effect refers to the phenomenon of a voltage being generated perpendicular to the direction of current flow in a magnetic field. In materials with two different types of charge carriers, the Hall coefficient and magnetoresistance can vary depending on the relative contributions of each type of carrier. This information can be used to determine the relative contributions of each band to the overall electronic and magnetic properties of the material.

5. What are the applications of knowing the two-band Hall coefficient and magnetoresistance?

The two-band Hall coefficient and magnetoresistance can provide valuable information for a wide range of applications, including the design and optimization of electronic and magnetic devices, understanding the behavior of materials under extreme conditions (such as high temperatures or strong magnetic fields), and investigating the electronic properties of semiconductors and superconductors.

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