Massive Dirac fermions and strong Shubnikov–de Haas oscillations in single crystals of the topological insulator Bi 2 Se 3 doped with Sm and Fe

Topological insulators (TIs) are emergent materials with unique band structure, which allow the study of quantum effect in solids, as well as contribute to high-performance quantum devices. To achieve the better performance of TIs, here, we present a codoping strategy using synergistic rare-earth (RE) Sm and transition-metal Fe dopants in ${\mathrm{Bi}}_{2}{\mathrm{Se}}_{3}$ single crystals, which combine the advantages of both a transition-metal-doped TI [high ferromagnetic ordering temperature and observed quantum anomalous Hall effect (QAHE)], and a RE doped TI (large magnetic moments and significant spin-orbit coupling). In the as-grown single crystals, clear evidences of ferromagnetic ordering were observed. The angle-resolve photoemission spectroscopy indicates the ferromagnetism opens a \ensuremath{\sim}44 meV band gap at the surface Dirac point. Moreover, the mobility of the carriers at 3 K is $\ensuremath{\sim}7400\phantom{\rule{0.16em}{0ex}}\mathrm{c}{\mathrm{m}}^{2}/\mathrm{Vs}$, and we thus observed an ultra-strong Shubnikov--de Haas oscillation in the longitudinal resistivity, as well as the Hall steps in transverse resistivity 14 T. Our transport and angular-resolved photoemission spectroscopy results suggest that the RE and transition metal codoping in the ${\mathrm{Bi}}_{2}{\mathrm{Se}}_{3}$ system is a promising avenue to implement the QAHE, as well as harnessing the massive Dirac fermion in electrical devices.