We present a calculation methodology of classical Hall mobility based on the non-equilibrium Green’s function method, and calculate the Hall mobility in two-dimensional systems without and with potential disorders. By using the Büttiker probe method, inelastic scattering is taken into account. The Hall mobility in systems without disorders agrees with the expectation by the scattering rate, validating our methodology. Then, the Hall mobility in systems with disorders is simulated, and the behavior is discussed by comparing with the results by Fermi’s golden rule, a scattering theory, and an analysis based on an average effective mass calculated considering the disorders. Reasonable agreement between the Hall mobility by the non-equilibrium Green’s function method and the estimation by the average effective mass is obtained, suggesting that the average effective mass can be used to estimate the Hall mobility in systems with disorders.

中文翻译：

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二维无序系统中霍尔迁移率的分析

我们提出了一种基于非平衡格林函数方法的经典霍尔迁移率的计算方法，并计算了在有无潜在障碍的二维系统中的霍尔迁移率。通过使用Büttiker探针方法，可以考虑非弹性散射。无障碍系统中的霍尔迁移率与散射率的预期吻合，验证了我们的方法。然后，模拟了具有障碍的系统中的霍尔迁移率，并通过与费米黄金定律，散射理论以及基于考虑到障碍的平均有效质量的分析进行比较，讨论了该行为。通过非平衡格林函数方法得出的霍尔迁移率与通过平均有效质量的估计值之间取得了合理的一致，