# What is Fermi sphere: Definition + 11 Threads

In condensed matter physics, the Fermi surface is the surface in reciprocal space which separates occupied from unoccupied electron states at zero temperature. The shape of the Fermi surface is derived from the periodicity and symmetry of the crystalline lattice and from the occupation of electronic energy bands. The existence of a Fermi surface is a direct consequence of the Pauli exclusion principle, which allows a maximum of one electron per quantum state.

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1. ### Relationship between k and E when deriving the density of states

Number of states in that volume of k-space, ##n(k)dk## is: $$n(k)dk = (\frac{L^3}{4 \pi^3}) \cdot 4 \pi k^2 dk = \frac{L^3}{\pi^2}dk$$. Then the notes state that by defintion, ##n(k)dk = n(E)dE##, and hence $$n(E)d(E) = \frac{L^3}{\pi^2}dk$$. I don't quite see why this is true - isn't it the...
2. ### I Fermi sphere and density of states

Hello! When computing the density of states of electrons in a lattice, a material with dimensions L_x, L_y, L_z can be considered. The allowed \mathbf{k} vectors will have components k_x = \displaystyle \frac{\pi}{L_x}p k_y = \displaystyle \frac{\pi}{L_y}q k_z = \displaystyle \frac{\pi}{L_z}r...
3. ### A Fermi energy Ef changes with applied electric field?

Hi people, I don't understand why when we apply the electric field to the metal Ef remains the same. Ef as translation energy of electrons remains the same but we accelerate the electrons with applied electric field so the translation energy increases too? In other hand according the formula...
4. ### F.E.G. fermi sphere radius problem

Homework Statement Calculate the electron concentrations (# electrons/atom) needed for the fermi sphere to contact the zone faces (first bril. zone edges) in BCC and FCC structures. Homework Equations kf = (3*pi^2*n)^(1/3) where n is # electrons per atom. For cubic structures...
5. ### How Do You Integrate Over the Fermi Sphere in 2D?

Homework Statement Hi I have the following integral over wavevectors inside the Fermi circle (we are in 2D) \int {dk_x \int {dk_y \sin ^2 \left( {k_x x} \right)} } Ok, so I know that kx2+ky2=kf2, so ky2=kf2-kx2 - this takes care of ky. But what about kx? What should this run from in order...
6. ### Why Integrate 0 to k0 for the Fermi Sphere?

I'd really appreciate any insight on any of this since I've hit a wall. It is about the Fermi gas. --- My teacher did an example in class that didn't make much sense, and I'm trying to understand it. He had us take the real-part of the antiderivative of exp(ik(x-x'))dk, then evaluate it to...
7. ### What is the Radius of Fermi Sphere for a 2D metal?

Homework Statement Problem 9.2(B) from Kittel Solid State Physics. A two-dimensional metal has one atom of valence one in a simple rectangular primitive cell of a1 = 2Å and a2 = 4Å. Calculate the radius of the free electron Fermi sphere and draw this sphere to scale on the drawing of the...
8. ### Maybe because is Fermi sphere is centered in origin?

In the theory of superconductivity BCS theory is given eigen - problem -\frac{\hbar^2}{2m}(\Delta_{\vec{r}_1}+\Delta_{\vec{r}_2})\psi(\vec{r}_1-\vec{r}_1)=(E+2\frac{\hbar^2k^2_F}{2m})\psi(\vec{r}_1-\vec{r}_1) Why E+2\frac{\hbar^2k^2_F}{2m}? Maybe because is Fermi sphere is centered in...
9. ### Understanding Fermi Sphere: Deriving Fermi Energy

Hi all, I'm studying on the current transfer at quantum level and I have a point that is not so much clear. While reading the Fermi sphere from the book "Current at the nanoscale", I could not understand the expression: The number of electrons in the conductor, N, is the ratio of the...
10. ### Why Is the Radius of a Fermi Sphere Given by $$k_F = (3 \pi^2 n)^{1/3}$$?

[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 k_F = \left(3 \pi^2 n \right)^{1/3} where n is the concentration of electrons. I don't know why that is true. EDIT: never mind; they derive that on...
11. ### Relaxation time = displacement lifetime of fermi sphere?

Homework Statement I just want to clear this up, I am a little confused: when an electric field is applied there is a force on the electron K-states thus displacing the fermi surface/sphere Is the relaxation time ( \tau)= lifetime of fermi sphere displacement or is lifetime of...