A variational approach is used in order to study the stationary states of Hall devices. Charge accumulation, electric potentials and electric currents are investigated on the basis of the Kirchhoff-Helmholtz principle of least heat dissipation. A simple expression for the state of minimum power dissipated -- that corresponds to zero transverse current and harmonic chemical potential -- is derived. It is shown that a longitudinal surface current proportional to the charge accumulation is flowing near the edges of the device. Charge accumulation and surface currents define a boundary layer over a distance of the order of the Debye-Fermi length.

中文翻译：

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霍尔器件中的表面电流

使用变分方法来研究霍尔器件的稳态。根据基尔霍夫-亥姆霍兹最小散热原理研究电荷积累、电势和电流。导出了最小功耗状态的简单表达式——对应于零横向电流和谐波化学势——。结果表明，与电荷积累成正比的纵向表面电流在器件边缘附近流动。电荷积累和表面电流在德拜-费米长度数量级的距离上定义了边界层。