Synchronous and Asynchronous Mott Transitions in Topological Insulator Ribbons

We address how the nature of linearly dispersing edge states of two dimensional (2D) topological insulators evolves with increasing electron-electron correlation engendered by a Hubbard like on-site repulsion $U$. We consider finite ribbons of two systems of topological band insulators with local electronic interactions incorporated. Using an inhomogeneous cluster slave rotor mean-field method developed here, we show that electronic correlations drive the topologically nontrivial phase into a Mott insulating phase via two different routes. In a synchronous transition, the entire ribbon attains a Mott insulating state at one critical $U$. In the second, asynchronous route, Mott localization first occurs on the edge layers at a smaller critical value of electronic interaction which then propagates into the bulk as $U$ is futher increased until all layers of the ribbon become Mott localized.