Advanced Solid State Physics

Outline

Electrons

Magnetic effects and
Fermi surfaces

Magnetism

Linear response

Transport

Crystal Physics

Electron-electron
interactions

Quasiparticles

Structural phase
transitions

Landau theory
of second order
phase transitions

Superconductivity

Quantization

Photons

Exam questions

Appendices

Lectures

Books

Course notes

TUG students

      

Free-electron model

In the free-electron model, the electron dispersion relation is,

\begin{equation} E(\vec{k})= \frac{\hbar^2 k^2}{2m^*}. \end{equation}

Here $m^*$ is the effective mass. At low temperatures, all of the $k$ states below the Fermi wave vector $k_F$ are filled and all the states above $k_F$ are empty. The electron density is the volume of the Fermi sphere, times two for spin, divided by the $k$-space volume per state,

\begin{equation} n =\frac{2}{(2\pi)^3}\frac{ 4\pi k_F^3}{3}=\frac{k_F^3}{3\pi^2}. \end{equation}

Many equilibrium thermodynamic properties of the free electron model depend only on the electron density and the effective mass. The transport properties of the free electron model depend on the electron density $n$, the effective mass $m^*$ and the relaxation time $\tau$.