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

In summary, the conversation discusses the difference between two pictures in Ashcroft & Mermin solid state physics book and how the + and - signs may not be compatible with each other. It is explained that the B field is reversed in the second picture, causing charges to appear off. The conversation also touches on the direction of the H field and Js in the two pictures and how they differ. It is noted that the drawings may not be well thought out and that the second picture is trying to explain the unusual behavior seen in the first picture. The conversation concludes with a statement about how the two diagrams are about one thing and should be similar to each other.
  • #1
Rzbs
52
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TL;DR Summary
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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  • #2
Its OK. The B field is reversed which is why charges may appear off.
 
  • #3
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?
 
  • #4
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.
 
  • #5
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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  • #6
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 postive hall coefficient and behaviour of magnetoresistance.
 
  • #7
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).
 

1. What is the Hall Effect in solid state physics?

The Hall Effect is a phenomenon in which a magnetic field applied perpendicular to an electric current in a conductor results in a voltage perpendicular to both the current and the magnetic field. This effect is commonly observed in solid state materials, such as semiconductors and metals.

2. How is the Hall Effect explained in Ashcroft & Mermin's book on solid state physics?

In their book, Ashcroft & Mermin explain the Hall Effect using the semiclassical model, which combines classical mechanics and quantum mechanics. They also introduce the concept of a Fermi surface, which is the boundary between occupied and unoccupied energy states in a solid. The movement of electrons within the Fermi surface under the influence of a magnetic field is what causes the Hall Effect.

3. What is the significance of the Hall Effect in solid state physics?

The Hall Effect is an important tool for studying the electronic properties of solid state materials, such as their conductivity and carrier mobility. It is also used in various applications, such as Hall sensors for measuring magnetic fields and Hall thrusters in spacecraft propulsion.

4. Can the Hall Effect be observed in all solid state materials?

No, the Hall Effect is only observed in materials with a finite number of charge carriers, such as metals and semiconductors. Insulators, which have no mobile charge carriers, do not exhibit the Hall Effect.

5. How does temperature affect the Hall Effect in solid state materials?

At low temperatures, the Hall Effect is dominated by the movement of electrons within the Fermi surface. However, at higher temperatures, thermal energy can cause electrons to jump between different energy states, making the Hall Effect more complex. This is known as the anomalous Hall Effect and is an active area of research in solid state physics.

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