Scanning tunneling spectroscopic (STS) studies of magnetically doped MBE-grown topological insulators (TIs)

We conduct STS studies on MBE-grown heterostructures of non-magnetic TI (Bi$_{2}$Se$_{3})$ with a range of thicknesses ($d =$ 1, 3, 5, 7 quintuple layers, QL) on top of 7-QL magnetically doped TI (Cr-doped Bi$_{2}$Se$_{3})$. For $d =$ 1 and 3-QL, a spatially homogeneous magnetism-induced surface gap (as large as about 150 meV for $d$ $=$ 1-QL) is observed at 77 K, whereas gapless Dirac spectra are found for $d =$ 5 and 7-QL, suggesting that the effective magnetic length for Cr-doped Bi$_{2}$Se$_{3}$ is approximately 4 $\sim$ 5-QL. These findings are further corroborated by ARPES and bulk electrical transport measurements. The magnetism-induced surface gap differs from those found in pure Bi$_{2}$Se$_{3}$ and (Bi$_{0.5}$Sb$_{0.5})_{2}$Te$_{3}$ films of thicknesses smaller than 6-QL, because the latter are due to overlaps of wave functions between the surface and interface layers, which lead to Rashba-like spin-orbit splitting and spin-preserving quasiparticle interference wave-vectors. In contrast, STS studies of TIs with magnetism-induced surface gap do not yield any quasiparticle interferences for energies within the bulk Bi$_{2}$Se$_{3}$ gap. Finally, comparative STS studies of pure and magnetically doped TIs in high magnetic fields will be discussed.