Quantum spin Hall insulator on the honeycomb lattice induced by ferromagnetic exchange interaction

• Published in: arXiv.org 2023-01
• Main Authors: Ye-Un An, Song-Jin, O, Kwang-Il Ryom, Il-Gwang Son
• Format: Article
• Language: English
• Subjects: Charge density waves; Exchanging; Ferromagnetism; Phase diagrams; Unity
• ISSN: 2331-8422
• DOI: 10.48550/arxiv.2301.09838

We study the many-body instabilities of correlated electrons on the half-filled honeycomb lattice with enhanced exchange coupling. The system is described by an extended Hubbard model including the next-nearest-neighbor Coulomb repulsion (\(V_2\)) and the nearest-neighbor exchange interaction (\(J\)). We use the truncated unity functional renormalization group approach to determine a schematic ground-state phase diagram with higher resolution in the parameter space of \(V_2\) and \(J\). In the absence of the on-site repulsion and presence of sizable next-nearest-neighbor repulsion and enhanced nearest-neighbor exchange interaction, we encounter the quantum spin Hall phase, the spin-Kekul\'{e} phase, and the three-sublattice and the incommensurate charge-density-wave phases. We propose a scheme for combining consistently the truncated unity functional renormalization group and the mean-field approximation, which is distinct from the conventional one that directly uses the renormalization-group results as an input for the mean-field calculation. This scheme is used to study in detail the quantum spin Hall phase, presenting some characteristics like the bulk gap, the Chern number and the helical edge states.