Evidence of topological gap opening in the surface state of Bi$_2$Se$_3$ by proximity to a magnetic insulator

Topological insulators are bulk insulators with exotic surface states, protected under time-reversal symmetry, that hold promise in observing many exciting condensed-matter phenomena. In this report, we show that by having a topological insulator (Bi$_2$Se$_3$) in proximity to a magnetic insulator (EuS), a metal-to-insulator transition in the surface state, attributed to opening of an exchange gap, can be observed whose properties are tunable using bottom gate voltage and external magnetic field. Our study provides evidence of gate-controlled enhanced interface magnetism with the signature of half-integer quantum Hall effect when the Fermi level is tuned into the exchange gap. These results pave the way for using magnetic proximity effect in developing topological electronic devices.