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<p>The internal energy and heat capacity of a two-dimensional electron gas in a half-filled Landau subband for a Gaussian distribution of the density of states are studied by analytical and numerical methods. Within the limits of low <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10773_2025_6115_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="78" /> </InlineMediaObject> <EquationSource Format="TEX">\(\:{k}_{B}T&lt;&lt;{\Gamma\:}\)</EquationSource> </InlineEquation> and high <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10773_2025_6115_Article_IEq2.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="78" /> </InlineMediaObject> <EquationSource Format="TEX">\(\:{k}_{B}T&gt;&gt;{\Gamma\:}\)</EquationSource> </InlineEquation> temperatures, analytical formulas for internal energy and heat capacity were found. The reason for the appearance of a peak in the temperature dependences of heat capacity is discussed. It is shown that in the region of <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10773_2025_6115_Article_IEq3.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="69" /> </InlineMediaObject> <EquationSource Format="TEX">\(\:{k}_{B}T\ge\:{\Gamma\:}\)</EquationSource> </InlineEquation>, saturation of the internal energy of the electron gas is observed due to the narrowness of the subband width. The analytical results are graphically compared with the numerical data.</p>

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Internal Energy and Heat Capacity of a Two-Dimensional Electron Gas in a Half-Filled Landau Subband

  • 期刊论文

  • 发表日期：

    2025年9月3日

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  • B. T. Abdulazizov,
  • P. J. Baymatov,
  • O. M. Yunusov,
  • Kh. N. Juraev,
  • M. S. Tokhirjonov

摘要

The internal energy and heat capacity of a two-dimensional electron gas in a half-filled Landau subband for a Gaussian distribution of the density of states are studied by analytical and numerical methods. Within the limits of low \(\:{k}_{B}T<<{\Gamma\:}\) and high \(\:{k}_{B}T>>{\Gamma\:}\) temperatures, analytical formulas for internal energy and heat capacity were found. The reason for the appearance of a peak in the temperature dependences of heat capacity is discussed. It is shown that in the region of \(\:{k}_{B}T\ge\:{\Gamma\:}\) , saturation of the internal energy of the electron gas is observed due to the narrowness of the subband width. The analytical results are graphically compared with the numerical data.