A numerical calculation of the temperature dependence of the chemical potential and for various values of the filling factor ν of the Landau level is carried out. The degree of filling of each Landau level is found as a function of temperature. Analytical calculations were carried out in the model of an ideal Fermi gas both without taking into account the broadening of the Landau levels Γ=0 and taking into account their broadening Γ>0. An analytical formula is found that describes the dependences of μ(T,ν) at Γ=0 and low temperatures. A low-temperature formula for the dependence of μ(T∕Γ,εF) based on the Sommerfeld expansion is also given. The influence of the intra- and interlevel thermal excitations on changes in the chemical potential with temperature is discussed.

中文翻译：

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磁场中二维电子气化学势的温度依赖性特征

化学势的温度依赖性和填充因子的各种值的数值计算ν朗道水平的进行。发现每个朗道水平的填充程度是温度的函数。分析计算是在理想费米气体模型中进行的，均未考虑朗道能级的展宽Γ=0并考虑到它们的扩展Γ>0. 找到了一个分析公式，描述了μ(吨,ν)在Γ=0和低温。低温依赖性的公式μ(吨∕Γ,εF)还给出了基于 Sommerfeld 展开的。讨论了层内和层间热激发对化学势随温度变化的影响。