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

A propagation matrix method is proposed to investigate spin-resolved electronic transport in single finger-gate (SFG) and double finger-gate (DFG) controlled split-gate quantum devices. We show how the interplay of the Rashba and Dresselhaus spin-orbit (SO) interactions as well as a Zeeman (Z) field influences the quantum transport characteristics. Without the Dresselhaus effect, the conductance reveals a mirror symmetry between the hole-like and the electron-like quasi-bound states in the SO-Z gap energy regime in the SFG system, but not for the DFG system. For the Dresselhaus interaction, we are able to analytically identify the binding energy of the SFG and DFG bound states. Furthermore, the DFG resonant states can be determined by tuning the distance between the finger gates.