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For nonparabolic dispersion law determined by the density of the energy states in a quantizing magnetic field, the dependence of the density of energy states on temperature in quantizing magnetic fields is studied with the nonquadratic dispersion law. Experimental results obtained for PbTe were analyzed using the suggested model. The continuous spectrum of the energy density of states at low temperature is transformed into discrete Landau levels.

In a study of the energy spectra of electrons in semiconductors, exceptional role was played by the application of quantum magnetic fields. As shown by Landau, in his classic work, the application of a magnetic field to a system of electrons causes a profound restructuring of the energy spectrum of electrons. It is accompanied by the appearance at certain values of the energy density of states singularities.

In the works of [

In the works of [

The aim of this work is to determine the temperature dependence of the density of energy states in a quantizing magnetic field for the model Kane and the effect of temperature of a sample on the results of treatment of experimental data.

In a magnetic field, the energy of free electrons with a quadratic dispersion law, and in view of the spinal level, splitting energy takes the following form [

Here, we have

In a magnetic field density of states for a parabolic band is determined by the following expression:

However, if the energy dependence of the wave vector is not described by a quadratic form, such as for electrons in InSb energy levels of the charge carriers in the magnetic field are not equidistant, since cyclotron mass is determined by the expression

Nonparabolicity conduction band in compounds III-IV and II–VI is the result of interaction between the conduction and valence bands. In magnetic field energy levels for the three bands (apart from the heavy hole band that does not interact with them) are cubic equation [

Here,

In our works, we consider narrow-gap semiconductors electrons that have a Kane dispersion law if the conditions [

From this condition of the cubic equation (

We now find the number of states with energies in the interval between Landau levels.

We define the difference between the areas of the cross sections of the two surfaces of constant energy, the energy of which differs by

The number of states per unit area in the plane of

From (

We return now to the calculation of the density of states with a nonparabolic dispersion law in a magnetic field. The movement of free electrons along the

As a result, we define the energy density of states per unit volume excluding spin Kane dispersion law in a magnetic field:

At

In the work of [

Thermal broadening of the levels in a magnetic field gives rise to the smoothing of discrete levels. Thermal broadening is to be taken into account using a derivative of the energy distribution function of the Fermi-Dirac

In order to take into account the temperature dependence of the density of states, we expend

Here,

The corresponding expression at

Density of energy states in a high magnetic field

Temperature dependence of the density of energy states in a quantizing magnetic field is calculated using a model Kane.

Let us consider the energy density of states of narrow-gap semiconductors in a quantizing magnetic field. Figure

Determination of the change in the density of energy states with decreasing temperature in high magnetic fields using the Kane model. (a) The experimental data (dots) for PbTe at

We developed a new method for determining the density of the energy states in a quantizing magnetic field for the Kane model. For a nonquadratic dispersion law, it was shown that the density of states in a strong magnetic field at an increased temperature coincides with the density of states in the sample without a magnetic field. It is shown that the Landau levels broaden due to the thermal effect as temperature is increased and

The authors declare that they have no competing interests.

_{0.86}Sb

_{0.14}/AlSb quantum wells