Radius of the fermi sphere

In summary, the radius of the Fermi sphere is a measure of the maximum distance an electron can have from the center of the sphere while still being considered part of the Fermi sea. It is calculated using the Fermi momentum, which is derived from the Fermi energy and the mass of the electron. This concept is significant in condensed matter physics and is used to describe the behavior of electrons in a material. As temperature increases, the Fermi energy and thus the radius of the Fermi sphere also increase. The radius of the Fermi sphere can be measured experimentally using various techniques such as ARPES and STM.
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ehrenfest
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[SOLVED] radius of the fermi sphere

Homework Statement


On page 249 of ISSP, Kittel says that the radius of a free electron Fermi sphere is

[tex]k_F = \left(3 \pi^2 n \right)^{1/3}[/tex]

where n is the concentration of electrons.

I don't know why that is true.

EDIT: never mind; they derive that on page 138

Homework Equations


The Attempt at a Solution

 
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1. What is the radius of the Fermi sphere?

The radius of the Fermi sphere is a measure of the maximum distance that an electron can have from the center of the sphere while still being considered part of the Fermi sea. It is defined by the Fermi momentum, which is the momentum of an electron at the Fermi energy.

2. How is the radius of the Fermi sphere calculated?

The radius of the Fermi sphere can be calculated using the Fermi momentum, which is derived from the Fermi energy and the mass of the electron. The formula for calculating the Fermi momentum is pF = √(2mEF), where m is the mass of the electron and EF is the Fermi energy.

3. What is the significance of the radius of the Fermi sphere?

The radius of the Fermi sphere is a fundamental concept in condensed matter physics and is used to describe the behavior of electrons in a material. It determines the maximum energy and momentum that electrons can have in a system and plays a crucial role in understanding the properties of metals and semiconductors.

4. How does temperature affect the radius of the Fermi sphere?

The radius of the Fermi sphere is directly related to the Fermi energy, which is temperature dependent. As the temperature of a material increases, the Fermi energy also increases, leading to an increase in the radius of the Fermi sphere. This means that at higher temperatures, more states are available for electrons to occupy within the Fermi sphere.

5. Can the radius of the Fermi sphere be measured experimentally?

Yes, the radius of the Fermi sphere can be measured experimentally using various techniques such as angle-resolved photoemission spectroscopy (ARPES) and scanning tunneling microscopy (STM). These methods allow for the observation of the Fermi surface, which is the two-dimensional projection of the Fermi sphere in momentum space.

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