Fermi Surface. Metals.


What is Fermi surface? Fermi surface in Fermi Gas model is a sphere. Limiting objects in 1dim, 2dim, 3dim.
Why is the area arround Fermi energy, i.e. the limit, important? Because only electrons in those states can change state due to thermal and other influences (the deep inside electrons have nowhere to go, all occupied). Electric and magnetic phenomena, Lorentz force.

In magnetic field, the charged particle cannot gain or lose energy. Reminder: equal-energy lines in the simple 2-dim band model: from circles to squares.
The evaluation of closed curve motion. This is closed curve in k-space, can be spiral in x-space. Line, i.e. curve, which is a cut of Fermi surface by a plane perpendicular to the magnetic field direction. Use the semiclassic equations of motion. Time intervals, path intervals on the Fermi curve.

Circular integral of the path gives the period of the motion. Resulting circular frequency. Manipulation of the path integral leads surprisingly to the expression containing the derivative of the area enclosed by the curve. (more details in the note).
Right: Lorentz, Group velocity.
As a result an expression for a frequency is obtained.

The cyclotron frequency, the Larmor frequency. Cyclotron mass. There are whole ranges of cyclotron frequencies. Page 231 of Ashcroft/Mermin.

Drawings to Fermi limits constructions. Periodic representation of bands necessary. Simple exercise: compare the states inside the Brillouin zone and Fermi circle for 2-dim model in the limit of vanishing potential.

More on metals: polycrystals. Sizes of crystals: tens of microns.
Conductivity revisited: the relaxation time

Conductivity revisited: the relaxation time. Scattering on different types of obstacles. Temperature dependence different: Matthiesens rule. This is a model for temperature dependence of the electrical conductivity.