Spin transport in topological insulator nanoribbons sandwiched between two-dimensional magnetic materials*

Nontrivial band topology along with magnetism leads to some novel quantum phases. When time-reversal-symmetry is broken in 3D 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 Quantum Anomalous Hall (QAH) phase displays sidewall chiral edge states  which leads to the QAH effect. In a finite slab, contribution of the surfaces 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 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.