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The influence of pressure on the oscillations of Shubnikov-de Haas (ShdH) and de Haas-van Alphen (dHvA) in semiconductors is studied. Working formula for the calculation of the influence of hydrostatic pressure on the Landau levels of electrons is obtained. The temperature dependence of quantum oscillations for different pressures is determined. The calculation results are compared with experimental data. It is shown that the effect of pressure on the band gap is manifested to oscillations and ShdH and dHvA effects in semiconductors.

Currently a variety of experimental methods for the study of influence of pressure on the oscillations ShdH and dHvA are tested in new types of semiconductors. Most quantum oscillation phenomena in semiconductors are due to oscillation density of energy states in a strong magnetic field [

The works of [

The aim of this work is a theoretical study of the influence of hydrostatic pressure on the quantum oscillation phenomena in semiconductors.

Consider the dynamics of the free electron gas in a quantizing magnetic field. In the presence of a magnetic field parallel to the

Here,

For parabolic zone [

Hence, the cyclotron mass

We now find the number of states in the interval between two Landau levels. Using expression (

For the determination of the oscillation effects of ShdH and dHvA in the conduction band, primarily we must calculate the oscillations of the density of energy states in quantizing magnetic field. We will consider a box with large but finite sides

From (

Then

As a result, we determine the density of the energy states in the presence of a magnetic field to the sample with a parabolic dispersion law:

As is known, the band gap depends on the magnetic field, temperature, and pressure. The dependence of the semiconductor band gap at hydrostatic pressure changes as follows [

Here,

The dependence of the Fermi level from pressure can be written in the following form:

Then the derivative with respect to the energy from Fermi-Dirac distribution function has the following form:

The dependence of the effective mass from the hydrostatic pressure can be represented by the following expression [

It is known that in the case of the density of states Landau quantization is a periodic function of the magnetic field. This leads to oscillations ShdH and dHvA that are periodic in the strong magnetic field. The relaxation time takes the following form:

Now, we must determine the critical pressure (

Now, we get the graphics effects oscillations ShdH and dHvA by means of formulas (

Comparison of oscillations effects of ShdH in Si at different pressures.

The dependence of the longitudinal magnetoresistance on hydrostatic pressure in Si.

Influence of the hydrostatic pressure on the oscillations of magnetosusceptibility in Si.

Influence of pressure on the temperature dependence of the oscillations ShdH in Si.

Temperature dependence of the oscillations ShdH in Si. (a) At no pressure; (b) at the pressure,

The work of [

Oscillations effects of ShdH in HgSe_{0.896}S_{0.104} at

Here,

Here,

As a result, we obtain graph dependence of the effect of oscillations ShdH on the pressure in Hg_{0.896}S_{0.104} at

The influence of pressure and temperature on the oscillations effects of ShdH and dHvA is considered in semiconductor. An analytical expression for the longitudinal magnetoresistance in semiconductors with Kane dispersion law for electrons is obtained. The calculation results are compared with experimental data. It is shown that the effect of pressure on the band gap is manifested to oscillations and ShdH and dHvA effects in semiconductors. The above results are valid when there is not any Lifshitz transition or any other pressure-induced phase transition.

The authors declare that they have no conflicts of interest.

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_{0.7}as heterostructures under conditions of the quantum hall effect