In this work, we investigate the existence of a thermoelectric effect that consists of the appearance of an electric field in one layer when a temperature gradient is applied in the other layer of a double quantum well system. This represents a generalization of the Seebeck effect to the case of two spatially separated electron systems allowed to interact only through the Coulomb repulsion. The induced electric field results from the momentum transfer between the electrons driven out of equilibrium by the temperature gradient and the electrons at rest in the passive layer, a mechanism known in the literature as the Coulomb drag. The rate of momentum transfer is calculated from the Fermi's golden rule applied to a screened Coulomb interaction. The electric field is found to be parallel to and proportional with the temperature gradient. The magnitude of the proportionality constant, an effective Seebeck coefficient, is estimated from the solutions of the Boltzmann transport equation in the two layers. Our result indicates a linear temperature variation, characteristic to degenerate Fermi systems, while the dependence on the distance between the layers introduces the geometric characteristics of the problem.
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