Phase Diagram and Crossover Phases of Topologically Ordered Graphene Zigzag Nanoribbons: Role of Localization Effects

TL;DR

This paper maps the phase diagram of zigzag graphene nanoribbons, revealing how topological order transitions into various disordered phases influenced by localization, doping, and repulsion, with implications for fractional charges and edge states.

Contribution

It introduces a detailed phase diagram showing crossover phases and the effects of localization and interactions on topological order in graphene nanoribbons.

Findings

Topological phases transition into crossover phases with nonuniversal entanglement entropy.

Strong interactions weaken nonlocal edge correlations and topological order.

Fractional charges and edge state properties vary across different phases.

Abstract

We computed the phase diagram of the zigzag graphene nanoribbons as a function of on-site repulsion, doping, and disorder strength. The topologically ordered phase undergoes topological phase transitions into crossover phases, which are new disordered phases with a nonuniversal topological entanglement entropy with significant variance. The topological order is destroyed by competition between localization effects and on-site repulsion. We found that strong on-site repulsion and/or doping weakens the nonlocal correlations between the opposite zigzag edges. In one of the crossover phases, both $\frac{e^-}{2}$ fractional charges and spin-charge separation were absent; however, charge-transfer correlations between the zigzag edges were possible. Another crossover phase contains $\frac{e^-}{2}$ fractional charges, but no charge transfer correlations. In low-doped zigzag ribbons the interplay between electron localization and on-site repulsion contributes to the spatial separation of quasi-degenerate gap-edge states and protects the charge fractionalization against quantum fluctuations. In all these effects, mixed chiral gap-edge states play an important role. The properties of nontopological strongly disordered and strongly repulsive phases are also observed. Each phase of the phase diagram has a different zigzag-edge structure. Additionally, we investigated the tunneling of solitonic fractional charges under an applied voltage between the zigzag edges of undoped topologically ordered zigzag ribbons, and found that it may lead to a zero-bias tunneling anomaly.