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We study theoretically the spin-Hall effect as well as its reciprocalphenomenon (a transverse charge current driven by a spin-dependent chemicalpotential gradient) in electron and hole finite size mesoscopic systems. TheLandauer-Buttiker-Keldysh formalism is used to model samples with mobilitiesand Rashba coupling strengths which are experimentally accessible and todemonstrate the appearance of measurable charge currents induced by thespin-dependent chemical potential gradient in the reciprocal spin-Hall effect.We also demonstrate that within the mesoscopic coherent transport regime theOnsager relations are fulfilled for the disorder averaged conductances forelectron and hole mesoscopic systems.

Charge Hall effect driven by spin-dependent chemical potential gradients and Onsager relations in mesoscopic systems