Bulk Rashba spin splitting and Dirac surface state in $p$-type (Bi$_{0.9}$Sb$_{0.1})_2$Se$_3$ single crystal

We report bulk Rashba spin splitting (RSS) and associated Dirac surface state in (Bi$_{0.9}$Sb$_{0.1})_2$Se$_3$, exhibiting dominant $p$-type conductivity. We argue from the synchrotron diffraction studies that origin of the bulk RSS is due to a structural transition to a non-centrosymmetric $R3m$ phase below $\sim$ 30 K. The Shubnikov-de Haas Van (SdH) oscillations observed in the magnetoresistance curves at low temperature and the Landau level fan diagram, as obtained from these oscillations, confirm the presence of nontrivial Dirac surface state. The magnetization data at low temperature exhibit substantial orbital magnetization consistent with the bulk RSS. The existance of both the bulk RSS and Dirac surface states are confirmed by first principles density functional theory calculations. Coexistence of orbital magnetism, bulk RSS, and Dirac surface state is unique for $p$-type (Bi$_{0.9}$Sb$_{0.1})_2$Se$_3$, making it an ideal candidate for spintronic applications.