Electrons in finite superlattices: the birth of crystal momentum

Properties of electrons in superlattices (SLs) of a finite length are described using standing waves resulting from the fixed boundary conditions (FBCs) at both ends. These electron properties are compared with those predicted by the standard treatments using running waves (Bloch states) resulting from the cyclic boundary conditions (CBCs). It is shown that, while the total number of eigenenergies in a miniband is the same according to both treatments, the number of different energies is twice higher according to the FBCs. It is also shown that the wave vector values corresponding to the eigenenergies are spaced twice as densely for the FBCs as for the CBCs. The reason is that a running wave is characterized by a single value of wave vector k, while a standing wave in a finite SL is characterized by a pair of wavevectors +/- q. Using numerical solutions of the Schroedinger equation for an electron in an increasing number N of periodic quantum wells (beginning with N = 2) we investigate the birth of an energy miniband and of a Brillouin zone according to the two approaches. Using the Fourier transforms of the computed wave functions for a few quantum wells we follow the birth of electrons momentum. It turns out that the latter can be discerned already for a system of two wells. We show that the number of higher values of the wave vector q involved in an eigenenergy state is twice higher for a standing wave with FBCs than for a corresponding Bloch state. Experiments using photons and phonons are proposed to observe the described properties of electrons in finite superlattices.

Temperature dependence of the electron spin g factor in GaAs

The temperature dependence of the electron spin $g$ factor in GaAs is investigated experimentally and theoretically. Experimentally, the $g$ factor was measured using time-resolved Faraday rotation due to Larmor precession of electron spins in the temperature range between 4.5 K and 190 K. The experiment shows an almost linear increase of the $g$ value with the temperature. This result is in good agreement with other measurements based on photoluminescence quantum beats and time-resolved Kerr rotation up to room temperature. The experimental data are described theoretically taking into account a diminishing fundamental energy gap in GaAs due to lattice thermal dilatation and nonparabolicity of the conduction band calculated using a five-level kp model. At higher temperatures electrons populate higher Landau levels and the average $g$ factor is obtained from a summation over many levels. A very good description of the experimental data is obtained indicating that the observed increase of the spin $g$ factor with the temperature is predominantly due to bands nonparabolicity.