Emerging weak localization effects on a topological insulator--insulating ferromagnet (Bi$_{2}$Se$_{3}$-EuS) interface*

A topological insulator (TI) has a full energy gap in the bulk, and possesses gapless Dirac-like surface states. Because of time reversal symmetry, the surface states cannot be back-scattered by non-magnetic impurities [1]. When a thin magnetic layer is applied on the surface, a full insulating gap is opened, and an electric charge close to the surface is predicted to induce an image magnetic monopole [2]. To further elucidate the uniqueness of transport in the surface state of TI materials, and to investigate such predicted interplay with magnetic materials, we studied the interface between a thin film TI (Bi$_{2}$Se$_{3})$ and an insulating ferromagnet (EuS). While above the Curie temperature ($T_{C})$ of the EuS we observed positive magnetoresistance (MR), which is obtainted ubiquitously in similar TI thin films and interpreted as weak antilocalization (WAL) effects [3], below $T_{C}$ the MR becomes negative near zero field, clearly indicating a proximity effect between the TI and the IF [4]. This phenomenon is consistent with recent theories that predict weak localization (WL) effects in TIs resulted from gap-opening at their surface state Dirac point [5,6].\\[4pt] [1] X.-L. Qi and S.-C. Zhang, Rev. Mod. Phys. \textbf{83}, 1057 (2011).\\[0pt] [2] J. E. Moore, Nature \textbf{464}, 194 (2010). \\[0pt] [3] H.-T. He, G. Wang, T. Zhang, I.-K. Sou, G. K. L. Wong, J.-N. Wang, H.-Z. Lu, S.-Q. Shen, and F.-C. Zhang, Phys. Rev. Lett. \textbf{106}, 166805 (2011).\\[0pt] [4] Q. I. Yang, M. Dolev, L. Zhang, J. Zhao, A. D. Fried, E. Schemm, M. Liu, A. Palevski, A. F. Marshall, S. H. Risbud, and A. Kapitulnik, Phys. Rev. B \textbf{88}, 081407 (2013).\\[0pt] [5] I. Garate and L. Glazman, Phys. Rev. B \textbf{86}, 035422 (2012).\\[0pt] [6] H.-Z. Lu, J. Shi, and S.-Q. Shen, Phys. Rev. Lett. \textbf{107}, 076801 (2011).