Electric field tunable spin-orbit gap in a bilayer graphene/WSe$_{2}$ quantum dot

We report on the investigation of proximity-induced spin-orbit coupling (SOC) in a heterostructure of bilayer graphene (BLG) and tungsten diselenide (WSe$_2$). A BLG quantum dot (QD) in the few-particle regime acts as a sensitive probe for induced SOC. Finite bias and magnetotransport spectroscopy measurements reveal a significantly enhanced SOC that decreases with the applied displacement field, distinguishing it from pristine BLG. We attribute this tunability to an increased layer localization of the QD states on the BLG layer distant to the WSe$_2$. Furthermore, our measurements demonstrate a reduced valley $g$-factor at larger displacement fields, consistent with a weaker lateral confinement of the QD. Our findings show evidence of the influence of WSe$_2$ across BLG layers, driven by reduced real-space confinement and increased layer localization at higher displacement fields. This study demonstrates the electrostatic tunability of spin-orbit gap in BLG/WSe$_2$ heterostructures, which is especially relevant for the field of spintronics and future spin qubit control in BLG QDs.