Fermi sphere Definition and 9 Threads

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...

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...

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...

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...

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...

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...

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...

[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...

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...