One hundred and forty years after his discovery, the Hall effect still deserves attention. If it is well-known that the Hall voltage measured in Hall bar devices is due to the electric charges accumulated at the edges in response to the magnetic field, the nature of the corresponding boundary conditions is still problematic. In order to study this out-of-equilibrium stationary state, the Onsager's least-dissipation principle is applied. It is shown that, beside the well-known expression of the charge accumulation and the corresponding Hall voltage, a longitudinal surface current proportional to the charge accumulation is generated. An expression of the surface current is given. The surface currents allow the Hall voltage to be stabilized at a stationary state, despite, e.g., the presence of leakage of charges at the edges.
We study the stationary state of Hall devices composed of a load circuit connected to the lateral edges of a Hall bar. We follow the approach developed in a previous work [Creff et al., J. Appl. Phys. 128, 054501 (2020)] in which the stationary state of an ideal Hall bar is defined by the minimum power dissipation principle. The presence of both the lateral circuit and the magnetic field induces the injection of a current: the so-called Hall current. Analytical expressions for the longitudinal and transverse currents are derived. It is shown that the efficiency of the power injection into the lateral circuit is quadratic in the Hall angle and obeys to the maximum transfer theorem. For usual values of the Hall angle, the main contribution of this power injection provides from the longitudinal current flowing along the edges instead of the transverse current crossing the Hall bar.
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