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.
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
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...
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...
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...