Quantum Phase Transition in Hall Conductivity on an Anisotropic Kagome Lattice

Abstract

We study the quantum Hall effect(QHE) on the Kagomé lattice with anisotropy in one of the hopping integrals. We find a new type of QHE characterized by the quantization rules for Hall conductivity ${\sigma }_{xy}=2n{e}^2/h$ and Landau Levels $E(n)=\pm v_F\sqrt{(n+1/2)\hslash Be}$ ($n$ is an integer), which is different from any known type. This phase evolves from the QHE phase with ${\sigma }_{xy}=4(n+1/2)e^2/h$ and $E(n)=\pm v_F\sqrt{2n\hslash Be}$ in the isotropic case, which is realized in a system with massless Dirac fermions (such as in graphene). The phase transition does not occur simultaneously in all Hall plateaus as usual but in sequence from low to high energies, with the increase of hopping anisotropy.

5 pages, 4 figures

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• RKKY plateau in zero- and one-dimensional triangular Kagome lattice models
• Nature of the 1/3 Magnetization Plateau in Spin-1/2 Kagome Antiferromagnets
• Recent progress in quantum spin liquids, fractional magnetization plateaus, and unconventional superconductivity in kagome lattices