Latent Haldane Models

TL;DR

This paper introduces a method to construct two-dimensional models that, through isospectral reduction, reveal energy-dependent Haldane and Semenoff masses, enabling the prediction of topological phases and gap-closing points in complex lattices.

Contribution

It presents a novel approach to generate energy-dependent topological models from complex 2D systems using isospectral reductions, without requiring staggered potentials.

Findings

Energy-dependent latent Haldane and Semenoff masses identified.

Phase diagrams constructed to locate topological phases.

Predictive method for topological phase transitions in decorated lattices.

Abstract

Latent symmetries, which materialize after performing isospectral reductions, have recently been shown to be instrumental in revealing novel topological phases in one-dimensional systems, among many other applications. In this work, we explore how to construct a family of seemingly complicated two-dimensional models that result in energy-dependent Haldane models upon performing an isospectral reduction. In these models, we find energy-dependent latent Semenoff masses without introducing a staggered on-site potential. In addition, energy-dependent latent Haldane masses also emerge in decorated lattices with nearest-neighbor complex hoppings. Using the Haldane model's properties, we then predict the location of the topological gaps in the aforementioned family of models and construct phase diagrams to determine where the topological phases lie in parameter space. This idea yielded, for instance, useful insights in the case of a modified version of $\alpha$-graphyne and hexagonal plaquettes with additional decorations, where the gap-closing energies can be calculated using the ISR to predict topological phase transitions.