Towards Joule heating optimization in Hall devices

We show that the Joule heating in Hall devices can be optimized by engineering the shape of the device. By using a geometrical method based on conformal transformations, we show the existence of two equivalence classes for Hall devices, exemplified by the Hall bar and the Corbino disk. The elements inside each class are related by means of a conformal mapping. Whereas the power dissipated by the systems of the Hall bar class formed by simply connected systems is conformally invariant and equal for each element of the class, that for systems of the Corbino disk class whose elements are doubly connected depends on their geometry and can thus be controlled by modifying the shape of the device. This general property could be used for a better performance of Hall devices.