Synchronous and Asynchronous Mott Transitions in Topological Insulator Ribbons

TL;DR

This paper investigates how electron-electron interactions induce Mott insulating phases in 2D topological insulator ribbons, revealing two distinct transition pathways—synchronous and asynchronous—dependent on edge state properties.

Contribution

It introduces an inhomogeneous cluster slave rotor mean-field method to analyze Mott transitions in topological insulator ribbons, identifying two different transition mechanisms.

Findings

Synchronous transition involves the entire ribbon becoming Mott insulator at a critical U.

Asynchronous transition starts with edge layers localizing first, then propagates inward.

Edge state properties determine the type of Mott transition occurring.

Abstract

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 $U$ in finite ribbons of two models of topological band insulators. 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 $U$ that depends weakly on the width of the ribbon. 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 further increased until all layers of the ribbon become Mott localized. We show that the kind of Mott transition that takes place is determined by certain properties of the linearly dispersing edge states which characterize the topological resilience to Mott localization.