Quantum anomalous Hall effect in d -electron kagome systems: Chern insulating states from transverse spin-orbit coupling

Physical review. B./Physical review. B, vol. 110

Abstract

The possibility of the quantum anomalous Hall effect (QAHE) in two-dimensional kagome systems with $d$-orbital electrons is studied within a multiorbital tight-binding model. We concentrate on the case of isotropic Slater-Koster integrals which is realized in a recently discovered class of metal-organic frameworks ${TM}_{3}{\mathrm{C}}_{6}{\mathrm{O}}_{6}$ with transition metals ($\mathit{TM}$) in the beginning of the $3d$ series. Furthermore, in the absence of exchange-type spin-orbit coupling, only isotropic Slater-Koster integrals give a perfect flatband in addition to the two dispersive bands hosting relativistic (Dirac) and quadratic band crossing points at high symmetry spots in the Brillouin zone. A quantized topological invariant requires a flux-creating spin-orbit coupling, giving Chern number (per spin sector) $C=1$ not only from the familiar Dirac points at the six corners of the Brillouin zone, but also from the quadratic band crossing point at the center $\mathrm{\ensuremath{\Gamma}}$. In the case of isotropic Slater-Koster integrals the on-site spin-orbit coupling (SOC) is ineffective in creating the QAHE and it is only the transfer or exchange-type SOC which can lead to a QAHE. Surprisingly, this QAHE comes from the nontrivial effective flux induced by the transverse part of the spin-orbit coupling, exhibited by electrons in the $d$-orbital state with ${m}_{l}=0$ (${d}_{{z}^{2}}$ orbital), in stark contrast to the more familiar form of QAHE due to the $d$ orbitals with ${m}_{l}\ensuremath{\ne}0$, driven by the Ising part of spin-orbit coupling. The $C=1$ Chern plateau (per spin sector) due to the Dirac point extends over a smaller region of Fermi energy than that due to quadratic band crossing. Our result hints at the promising potential of kagome $d$-electron systems as a platform for dissipationless electronics by virtue of its unique QAHE.

Authors 8

1. Imam Makhfudz

   Aix-Marseille Université · Institut des Matériaux, de Microélectronique et des Nanosciences de Provence

   Affiliation as printed

   Aix-Marseille Université

   IM2NP

2. Mikhail A. Cherkasskii Aachen

   RWTH Aachen University

   Affiliation as printed

   RWTH Aachen University

3. Mohammad Alipourzadeh

   Shahid Chamran University of Ahvaz

   Affiliation as printed

   Shahid Chamran University of Ahvaz

4. Yaser Hajati

   Shahid Chamran University of Ahvaz

   Affiliation as printed

   Shahid Chamran University of Ahvaz

5. P. Lombardo

   Aix-Marseille Université · Institut des Matériaux, de Microélectronique et des Nanosciences de Provence

   Affiliation as printed

   Aix-Marseille Université

   IM2NP

6. Steffen Schäfer

   Aix-Marseille Université · Institut des Matériaux, de Microélectronique et des Nanosciences de Provence

   Affiliation as printed

   Aix-Marseille Université

   IM2NP

7. Silvia Viola Kusminskiy Aachen

   Max Planck Institute for the Science of Light · RWTH Aachen University

   Affiliation as printed

   Max Planck Institute for the Science of Light

   RWTH Aachen University

8. R. Hayn

   Aix-Marseille Université · Institut des Matériaux, de Microélectronique et des Nanosciences de Provence

   Affiliation as printed

   Aix-Marseille Université

   IM2NP