Solid State Physics: Explaining Ashcroft & Mermin's Hall Effect

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SUMMARY

The forum discussion centers on the discrepancies between two diagrams in Ashcroft & Mermin's solid state physics book, specifically regarding the Hall Effect. Participants highlight that the diagrams illustrate different concepts, with the second diagram addressing the Hall Effect under high field strength conditions, which differs from the ordinary Hall Effect. Key points include the orientation of the magnetic field (B field) and the electric field (E field), as well as the implications of positive and negative charge carriers. The discussion emphasizes the need for clarity in scientific illustrations to enhance understanding.

PREREQUISITES
  • Understanding of the Hall Effect in solid state physics
  • Familiarity with magnetic field orientation and notation (e.g., circles with dots and crosses)
  • Knowledge of charge carriers and their behavior in magnetic fields
  • Basic principles of solid state physics as presented in Ashcroft & Mermin's textbook
NEXT STEPS
  • Study the Hall Effect under varying field strengths and its implications on material behavior
  • Research the differences between ordinary and high-field Hall Effect phenomena
  • Examine the role of charge carriers in magnetic fields, focusing on positive and negative carriers
  • Review the illustrations in Ashcroft & Mermin's solid state physics book for clarity and accuracy
USEFUL FOR

Students and educators in physics, particularly those focusing on solid state physics and the Hall Effect, as well as researchers exploring high-field phenomena in materials.

Rzbs
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TL;DR
Hall effect in the high-field limit
Could anyone please explain the differnce between these two picture of Ashcroft & Mermin solid state physics book:
Screenshot_20201106-163501.png
Screenshot_20201106-163413.png

Why in these two pictures the + and - signs don't compatible with each other?! I think in the pic12-11 the signs don't draw correctly. It must be vice versa I mean + signs in left and - signs in right?!
 
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Its OK. The B field is reversed which is why charges may appear off.
 
shjacks45 said:
Its OK. The B field is reversed which is why charges may appear off.
Thanks. So you say in the second picture the H field is along -z direction?

but It seems in two pictures the H fields are along +z direction and Js are along +x direction, but in the first picture Ey is along -y and in the next picture it's along +y! Why? What is my mistake?
 
Rzbs said:
Thanks. So you say in the second picture the H field is along -z direction?

but It seems in two pictures the H fields are along +z direction and Js are along +x direction, but in the first picture Ey is along -y and in the next picture it's along +y! Why? What is my mistake?
Second diagram had "B" next to a circle with a dot in it. If it was the other direction then it would be a circle with an x in it. Did you note that the two diagrams are about different things? They are not meant to be identical.
 
shjacks45 said:
Second diagram had "B" next to a circle with a dot in it. If it was the other direction then it would be a circle with an x in it. Did you note that the two diagrams are about different things? They are not meant to be identical.
I agree that the drawings are not well thought out but I didn't see the whole paper. Drawings should improve the quality of the paper, not obfuscate. Hall effect is a basic part of physics, BUT this paper was about Hall Effect at very high field strength and how it was different from ordinary Hall Effect normally encountered. Like anything at extremes (metallic Hydrogen at extreme Jupiter-like pressure) there are surprise changes in how materials behave.
 
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shjacks45 said:
Second diagram had "B" next to a circle with a dot in it. If it was the other direction then it would be a circle with an x in it.

I know the meaning of a circle with a dot or with an x. So in second diagram +z is outward of the page.

Did you note that the two diagrams are about different things? They are not meant to be identical

The two diagrams are in Ashcroft and Mermin solid state physics book in different chapters. The second one tried to explain the unusal behavior of the first one like positive hall coefficient and behaviour of magnetoresistance.
 
shjacks45 said:
I agree that the drawings are not well thought out but I didn't see the whole paper. Drawings should improve the quality of the paper, not obfuscate. Hall effect is a basic part of physics, BUT this paper was about Hall Effect at very high field strength and how it was different from ordinary Hall Effect normally encountered. Like anything at extremes (metallic Hydrogen at extreme Jupiter-like pressure) there are surprise changes in how materials behave.
The two diagrams are about one thing and I think should be like each other. Maybe in the second one the charge careers are positive (I'm not sure because the book don't say anything about this).
 

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