  Nontrivial band topology along with magnetism leads to different novel
quantum phases. When time-reversal-symmetry is broken in three-dimensional
topological insulators (TIs) by applying high enough magnetic field or
proximity effect, different phases such as quantum Hall or quantum anomalous
Hall(QAH) emerge and display interesting transport properties for spintronic
applications. The QAH phase displays sidewall chiral edge states which leads to
the QAH effect. In a finite slab, contribution of the surface states depends on
both the cross-section and thickness of the system. Having a small
cross-section and a thin thickness leads to direct coupling of the surfaces, on
the other hand, a thicker slab results in a higher contribution of the
non-trivial sidewall states which connect top and bottom surfaces. In this
regard, we have considered a heterostructure consisting of a TI, namely Bi2Se3,
which is sandwiched between two-dimensional magnetic monolayers of CrI3 to
study its topological and transport properties. Combining DFT and tight-binding
calculations along with non-equilibrium Green's function formalism, we show
that a well-defined exchange gap appears in the band structure in which spin
polarised edge states flow. We also study the width and finite-size effect on
the transmission and topological properties of this magnetised TI nanoribbon.
