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A propagation matrix method is proposed to investigate spin-resolvedelectronic transport in single finger-gate (SFG) and double finger-gate (DFG)controlled split-gate quantum devices. We show how the interplay of the Rashbaand Dresselhaus spin-orbit (SO) interactions as well as a Zeeman (Z) fieldinfluences the quantum transport characteristics. Without the Dresselhauseffect, the conductance reveals a mirror symmetry between the hole-like and theelectron-like quasi-bound states in the SO-Z gap energy regime in the SFGsystem, but not for the DFG system. For the Dresselhaus interaction, we areable to analytically identify the binding energy of the SFG and DFG boundstates. Furthermore, the DFG resonant states can be determined by tuning thedistance between the finger gates.

Single and double finger-gate controlled spin electronic transport with an in-plane magnetic field