# Quantum Phase Transition in Hall Conductivity on an Anisotropic Kagome Lattice - Condensed Matter > Mesoscale and Nanoscale Physics

Abstract: We study the quantum Hall effectQHE on the Kagom\-{e} lattice withanisotropy in one of the hopping integrals. We find a new type of QHEcharacterized by the quantization rules for Hall conductivity$\sigma {xy}=2ne^{2}-h$ and Landau Levels $En=\pm v {F}\sqrt{n+1-2\hbarBe}$ $n$ is an integer, which is different from any known type. This phaseevolves from the QHE phase with $\sigma {xy}=4n+1-2e^{2}-h$ and $En=\pmv {F}\sqrt{2n\hbar Be}$ in the isotropic case, which is realized in a systemwith massless Dirac fermions such as in graphene. The phase transition doesnot occur simultaneously in all Hall plateaus as usual but in sequence from lowto high energies, with the increase of hopping anisotropy.

Author: Shun-Li Yu, Jian-Xin Li, Li Sheng

Source: https://arxiv.org/