For semiconductor material in which density of free electrons is small, experiments on a cyclotron resonance can be executed with the electromagnetic waves getting into a solid body. Difficulty which thus arise, are connected with topology of surfaces of constant energy and with hybrid plasma resonances, in that case when concentration of free electrons is not too small.
Let's consider the movement equation for a case when the field B is directed along an axis z. For simplicity we will consider t® of ¥ and we will put E = we Will notice in passing that so simply it would be possible to solve the equations and for final t. The condition of existence of well expressed resonant line is satisfied at wct> 1 where wc is given by a formula (ÑÃÑ) of wczeb/mc. So, in the case under consideration equation,
According to Maxwell's equation, the magnetic field operating on an electron to seek to change the direction of the movement of an electron, without changing its energy. It follows from a formula for Lorentz force. Thus, the magnetic induction of Bz has impact on the movement in the xy plane, without changing the movement in the direction of z. If the electron does not dissipate, it describes some orbit the movement on which is imposed on any movement in the direction of z in the xy plane.
Under the influence of a magnetic field the movement of an electron in real space is followed by a precession in k-space on a trajectory with constant energy in Brillouin's zone. Of course, for very strongly degenerate electronic gas in metal this movement is observed only for electrons with Fermi's energy, i.e. for electrons which describe in orbit k-space round Fermi's surface. As some dispersion of electrons on phonons and defects is inevitable even in almost ideal crystal at low temperatures, distinctly expressed cyclotron movement can be received only on condition of (wctm)> 1 i.e. when the electron can take place considerable part of the magnetic orbit before it is disseminated.