A question For experts in Solid State Physics

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SUMMARY

The discussion centers on the conceptual understanding of Fermi surfaces and Fermi spheres in solid state physics, specifically in the context of one and two-dimensional electron gases. It is established that in one dimension, the Fermi surface consists of two planes separated by a distance of 2Kf. The terms "Fermi surface" and "Fermi sphere" are placed in quotation marks to indicate that they are mathematical abstractions rather than physical entities. The inquiry seeks clarification from experts in solid state physics, as standard references like Ashcroft and Mermin or Kittel do not provide satisfactory explanations.

PREREQUISITES
  • Understanding of electron gas behavior in solid state physics
  • Familiarity with Fermi surfaces and Fermi spheres
  • Knowledge of one-dimensional and two-dimensional systems
  • Basic grasp of mathematical abstractions in physics
NEXT STEPS
  • Study the concept of Fermi surfaces in one-dimensional systems
  • Explore the mathematical representations of Fermi spheres
  • Research the implications of electron gas behavior in two-dimensional materials
  • Examine advanced solid state physics textbooks, focusing on Ashcroft and Mermin
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Students and researchers in solid state physics, particularly those studying electron behavior in low-dimensional systems and seeking a deeper understanding of Fermi surfaces and spheres.

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Homework Statement


Consider an electron gas in ONE and TWO dimensions i.e N electrons in a metal wire with length L or in metal sheet with area L^2.

Pictures must be drwan of the fermi 'sphere' and the Fermi 'surface' .
Why are the two words in quotation marks ?

Homework Equations





The Attempt at a Solution


From hours of research i did on the WEB .(Im not by no means an expert in SOLID STATE PHYSICS), i managed to find only that in one Dimension the fermi surface is 2 planes separted by distance 2Kf.

Ascroft and Mermin as well as Kittel to my knowledge cannot answer this Question.
Any Experts in Solid state Physics who can Help ?
 
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The two words are in quotation marks because Fermi surfaces and Fermi spheres are not actually surfaces or spheres; they are mathematical abstractions used to conceptualize the behavior of electrons in a solid.
 

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