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The response of a metal to a magnetic field, , in the direction say,
has given considerable information
about the Fermi surface, because electrons follow a trajectory on the Fermi
surface in a plane of constant .
In these notes we discuss how free electron states are
modified by a magnetic field, and how this affects the energy of the system in
an oscillatory manner, provided certain conditions, given in
Eqs. (10) and
(11) below, are satisfied.
As is shown in standard texts on quantum mechanics, the energy levels of free
electrons in a magnetic field are modified from

(1) 
to

(2) 
where
and

(3) 
is the cyclotron frequency, i.e. the frequency of the classical motion.
The states with a given are known collectively as a
Landau level. The degeneracy of a Landau level is

(4) 
where is the area of the sample in the plane perpendicular to , the
factor of two in the first expression
comes from spin degeneracy, and

(5) 
is the flux quantum for a pair of electrons.
Next: Two dimensions, free electrons
Up: magnetic_field
Previous: magnetic_field
Peter Young
20021031